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75-404: A QR code ( quick-response code ) is a type of two-dimensional matrix barcode , invented in 1994, by Japanese company Denso Wave for labelling automobile parts. It features black squares on a white background with fiducial markers , readable by imaging devices like cameras, and processed using Reed–Solomon error correction until the image can be appropriately interpreted. The required data

150-403: A Web browser ). QR code has become a focus of advertising strategy, since it provides a way to access a brand's website more quickly than by manually entering a URL. Beyond mere convenience to the consumer, the importance of this capability is that it increases the conversion rate : the chance that contact with the advertisement will convert to a sale. It coaxes interested prospects further down

225-415: A brand protection program. However, the security level of a regular QR code is limited since QR codes printed on original products are easily reproduced on fake products, even though the analysis of data generated as a result of QR code scanning can be used to detect counterfeiting and illicit activity. A higher security level can be attained by embedding a digital watermark or copy detection pattern into

300-447: A camera phone equipped with the correct reader application can scan the image of the QR code to display text and contact information, connect to a wireless network , or open a web page in the phone's browser. This act of linking from physical world objects is termed hardlinking or object hyperlinking . QR codes also may be linked to a location to track where a code has been scanned. Either

375-555: A conformal map . The plane itself is homeomorphic (and diffeomorphic) to an open disk . For the hyperbolic plane such diffeomorphism is conformal, but for the Euclidean plane it is not. Conversion rate In electronic commerce , conversion marketing is marketing with the intention of increasing conversions— that is, site visitors who are paying customers . Conversion marketing attempts to solve low online conversions through optimized customer service , which requires

450-834: A headstone . In 2008, Ishinokoe in Yamanashi Prefecture, Japan began to sell tombstones with QR codes produced by IT DeSign, where the code leads to a virtual grave site of the deceased. Other companies, such as Wisconsin-based Interactive Headstones, have also begun implementing QR codes into tombstones. In 2014, the Jewish Cemetery of La Paz in Uruguay began implementing QR codes for tombstones. QR codes can be used to generate time-based one-time passwords for electronic authentication . QR codes have been used by various retail outlets that have loyalty programs . Sometimes these programs are accessed with an app that

525-421: A hyperbolic plane , which obeys hyperbolic geometry and has a negative curvature . Abstractly, one may forget all structure except the topology, producing the topological plane, which is homeomorphic to an open disk . Viewing the plane as an affine space produces the affine plane , which lacks a notion of distance but preserves the notion of collinearity . Conversely, in adding more structure, one may view

600-426: A line at infinity is appended to σ . As any line in this extension of σ corresponds to a plane through O , and since any pair of such planes intersects in a line through O , one can conclude that any pair of lines in the extension intersect: the point of intersection lies where the plane intersection meets σ or the line at infinity. Thus the axiom of projective geometry, requiring all pairs of lines in

675-440: A plane is a flat two- dimensional surface that extends indefinitely. Euclidean planes often arise as subspaces of three-dimensional space R 3 {\displaystyle \mathbb {R} ^{3}} . A prototypical example is one of a room's walls, infinitely extended and assumed infinitesimal thin. The elliptic plane is the real projective plane provided with a metric . Kepler and Desargues used

750-555: A QR code in its design which, when scanned with an internet-enabled mobile device, goes to the official Bank of Ghana website. Credit card functionality is under development. In September 2016, the Reserve Bank of India (RBI) launched the eponymously named BharatQR , a common QR code jointly developed by all the four major card payment companies – National Payments Corporation of India that runs RuPay cards along with Mastercard , Visa , and American Express . It will also have

825-412: A QR code is shown on the login page on a computer screen , and when a registered user scans it with a verified smartphone, they will automatically be logged in. Authentication is performed by the smartphone, which contacts the server. Google deployed such a login scheme in 2012. There is a system whereby a QR code can be displayed on a device such as a smartphone and used as an admission ticket . Its use

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900-515: A QR code or a barcode. Some 58% of those users scanned a QR or barcode from their homes, while 39% scanned from retail stores; 53% of the 14 million users were men between the ages of 18 and 34. In 2022, 89 million people in the United States scanned a QR code using their mobile devices, up by 26 percent compared to 2020. The majority of QR code users used them to make payments or to access product and menu information. In September 2020,

975-691: A QR code. Many of these applications target mobile-phone users (via mobile tagging ). Users may receive text, add a vCard contact to their device, open a URL, or compose an e-mail or text message after scanning QR codes. They can generate and print their own QR codes for others to scan and use by visiting one of several pay or free QR code-generating sites or apps. Google had an API , now deprecated, to generate QR codes, and apps for scanning QR codes can be found on nearly all smartphone devices. QR codes storing addresses and URLs may appear in magazines, on signs, on buses, on business cards, or on almost any object about which users might want information. Users with

1050-442: A cashier or waiter. QR codes can also link to daily or weekly specials that are not printed on the standardized menus, and enable the establishment to update the entire menu without needing to print copies. At table-serve restaurants, QR codes enable guests to order and pay for their meals without a waiter involved – the QR code contains the table number so servers know where to bring the food. This application has grown especially since

1125-541: A company's discounted and percent discount can be captured using a QR code decoder that is a mobile app, or storing a company's information such as address and related information alongside its alpha-numeric text data as can be seen in telephone directory yellow pages . They can also be used to store personal information for organizations. An example of this is the Philippines National Bureau of Investigation (NBI) where NBI clearances now come with

1200-400: A complex combination of personalized customer experience management, web analytics, and the use of customer feedback to contribute to process flow improvement and site design. By focusing on improving site flow, online customer service channels, and the online experience conversion marketing is commonly viewed as a long-term investment rather than a quick fix . Increased site traffic over

1275-421: A digital apostille is a PDF document with a cryptographic signature containing a QR code for a canonical URL of the original document, allowing users to verify the apostille from a printed version of the document. Different studies have been conducted to assess the effectiveness of QR codes as a means of conveying labelling information and their use as part of a food traceability system. In a field experiment, it

1350-418: A plane as a 2-dimensional real manifold , a topological plane which is provided with a differential structure . Again in this case, there is no notion of distance, but there is now a concept of smoothness of maps, for example a differentiable or smooth path (depending on the type of differential structure applied). The isomorphisms in this case are bijections with the chosen degree of differentiability. In

1425-421: A plane may be defined. The Euclidean plane follows Euclidean geometry , and in particular the parallel postulate . A projective plane may be constructed by adding "points at infinity" where two otherwise parallel lines would intersect, so that every pair of lines intersects in exactly one point. The elliptic plane may be further defined by adding a metric to the real projective plane. One may also conceive of

1500-474: A plane to intersect, is confirmed. In mathematics , a projective plane is a geometric structure that extends the concept of a plane . In the ordinary Euclidean plane, two lines typically intersect at a single point, but there are some pairs of lines (namely, parallel lines) that do not intersect. A projective plane can be thought of as an ordinary plane equipped with additional "points at infinity" where parallel lines intersect. Thus any two distinct lines in

1575-556: A projective plane intersect at exactly one point. Renaissance artists, in developing the techniques of drawing in perspective , laid the groundwork for this mathematical topic. The archetypical example is the real projective plane , also known as the extended Euclidean plane. This example, in slightly different guises, is important in algebraic geometry , topology and projective geometry where it may be denoted variously by PG(2, R) , RP , or P 2 (R), among other notations. There are many other projective planes, both infinite, such as

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1650-419: A result of subtle or direct requests from marketers, advertisers, and content creators. Successful conversions are defined differently by individual marketers, advertisers, and content creators. For online retailers, for example, a successful conversion may be defined as the sale of a product to a consumer whose interest in the item was initially sparked by clicking a banner advertisement . For content creators,

1725-469: A single label that contained the data of each label. The quadrangular configuration of the QR code system consolidated the data of the various bar-code labels with Kanji, Kana , and alphanumeric codes printed onto a single label. As of 2024, QR codes are used in a much broader context, including both commercial tracking applications and convenience-oriented applications aimed at mobile phone users (termed mobile tagging). QR codes may be used to display text to

1800-470: A smartphone and originally linked to a special website with content about the historical event and design of the coin. In 2014, the Central Bank of Nigeria issued a 100-naira banknote to commemorate its centennial, the first banknote to incorporate a QR code in its design. When scanned with an internet-enabled mobile device, the code goes to a website that tells the centenary story of Nigeria. In 2015,

1875-551: A successful conversion may refer to a membership registration, newsletter subscription, software download, or other activity. For websites that seek to generate offline responses, for example telephone calls or foot traffic to a store, measuring conversion rates can be difficult because a phone call or personal visit is not automatically traced to its source, such as the Yellow Pages, website, or referral. Possible solutions include asking each caller or shopper how they heard about

1950-581: A survey found that 18.8 percent of consumers in the United States and the United Kingdom strongly agreed that they had noticed an increase in QR code use since the then-active COVID-19 -related restrictions had begun several months prior. Several standards cover the encoding of data as QR codes: At the application layer , there is some variation between most of the implementations. Japan's NTT DoCoMo has established de facto standards for

2025-476: A web page showing the supply chain for each ingredient, as well as information specific to each related batch, including meat processors and manufacturers, which helps address the concerns they have about the origin of their food. After the COVID-19 pandemic began spreading, QR codes began to be used as a "touchless" system to display information, show menus, or provide updated consumer information, especially in

2100-462: Is x 8 + x 4 + x 3 + x 2 + 1 {\displaystyle x^{8}+x^{4}+x^{3}+x^{2}+1} , corresponding to the polynomial number 285, with initial root = 0. The Reed–Solomon code uses one of 37 different polynomials over F 256 {\displaystyle \mathbb {F} _{256}} , with degrees ranging from 7 to 68, depending on how many error correction bytes

2175-437: Is a geometric space in which two real numbers are required to determine the position of each point . It is an affine space , which includes in particular the concept of parallel lines . It has also metrical properties induced by a distance , which allows to define circles , and angle measurement . A Euclidean plane with a chosen Cartesian coordinate system is called a Cartesian plane . In Euclidean geometry ,

2250-561: Is a very popular and convenient method of making payments. Since Alipay designed a QR code payment method in 2011, mobile payment has been quickly adopted in China. As of 2018, around 83% of all payments were made via mobile payment. In November 2012, QR code payments were deployed on a larger scale in the Czech Republic when an open format for payment information exchange – a Short Payment Descriptor  – was introduced and endorsed by

2325-651: Is common for J1 League and Nippon Professional Baseball tickets in Japan. In some cases, rights can be transferred via the Internet. In Latvia , QR codes can be scanned in Riga public transport to validate Rīgas Satiksme e-tickets. Restaurants can present a QR code near the front door or at the table allowing guests to view an online menu, or even redirect them to an online ordering website or app, allowing them to order and/or possibly pay for their meal without having to use

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2400-503: Is currently expanding globally. Walmart, Procter & Gamble and Woolworths have already adopted the Virtual Store concept. QR codes can be used to store bank account information or credit card information, or they can be specifically designed to work with particular payment provider applications. There are several trial applications of QR code payments across the world. In developing countries including China, India QR code payment

2475-417: Is known as a (26,19,2) error correction code over GF(2) . Due to error correction, it is possible to create artistic QR codes with embellishments to make them more readable or attractive to the human eye, and to incorporate colors, logos, and other features into the QR code block; the embellishments are treated as errors, but the codes still scan correctly. Plane (mathematics) Several notions of

2550-465: Is loaded onto a phone and includes a process triggered by a QR code scan. The QR codes for loyalty programs tend to be found printed on the receipt for a purchase or on the products themselves. Users in these schemes collect award points by scanning a code. Serialised QR codes have been used by brands and governments to let consumers, retailers and distributors verify the authenticity of the products and help with detecting counterfeit products, as part of

2625-525: Is made at correcting more than 15 errors per block; this limits the complexity of the decoding algorithm. The code blocks are then interleaved together, making it less likely that localized damage to a QR symbol will overwhelm the capacity of any single block. The Version 1 QR symbol with level L error correction, for example, consists of a single error correction block with a total of 26 code bytes (made of 19 message bytes and seven error correction bytes). It can correct up to 2 byte errors. Hence, this code

2700-541: Is not the only geometry that the plane may have. The plane may be given a spherical geometry by using the stereographic projection . This can be thought of as placing a sphere tangent to the plane (just like a ball on the floor), removing the top point, and projecting the sphere onto the plane from this point. This is one of the projections that may be used in making a flat map of part of the Earth's surface. The resulting geometry has constant positive curvature. Alternatively,

2775-422: Is then extracted from patterns that are present in both the horizontal and the vertical components of the QR image. Whereas a barcode is a machine-readable optical image that contains information specific to the labeled item, the QR code contains the data for a locator, an identifier, and web-tracking. To store data efficiently, QR codes use four standardized modes of encoding: Compared to standard UPC barcodes ,

2850-699: The Central Bank of the Russian Federation issued a 100- rubles note to commemorate the annexation of Crimea by the Russian Federation . It contains a QR code into its design, and when scanned with an internet-enabled mobile device, the code goes to a website that details the historical and technical background of the commemorative note. In 2017, the Bank of Ghana issued a 5- cedis banknote to commemorate 60 years of central banking in Ghana . It contains

2925-988: The Czech Banking Association as the official local solution for QR payments. In 2013, the European Payment Council provided guidelines for the EPC QR code enabling SCT initiation within the Eurozone . In 2017, Singapore created a task force including government agencies such as the Monetary Authority of Singapore and Infocomm Media Development Authority to spearhead a system for e-payments using standardized QR code specifications. These specific dimensions are specialized for Singapore. The e-payment system, Singapore Quick Response Code (SGQR), essentially merges various QR codes into one label that can be used by both parties in

3000-455: The EU ( EU Digital COVID certificate ), where they can be scanned to verify the information on the certificate. Unlike the older, one-dimensional barcodes that were designed to be mechanically scanned by a narrow beam of light, a QR code is detected by a two-dimensional digital image sensor and then digitally analyzed by a programmed processor. The processor locates the three distinctive squares at

3075-465: The complex projective plane , and finite, such as the Fano plane . In addition to its familiar geometric structure, with isomorphisms that are isometries with respect to the usual inner product, the plane may be viewed at various other levels of abstraction . Each level of abstraction corresponds to a specific category . At one extreme, all geometrical and metric concepts may be dropped to leave

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3150-515: The conversion funnel with little delay or effort, bringing the viewer to the advertiser's website immediately, whereas a longer and more targeted sales pitch may lose the viewer's interest. Although initially used to track parts in vehicle manufacturing, QR codes are used over a much wider range of applications. These include commercial tracking, warehouse stock control, entertainment and transport ticketing, product and loyalty marketing, and in-store product labeling. Examples of marketing include where

3225-452: The gnomonic projection to relate a plane σ to points on a hemisphere tangent to it. With O the center of the hemisphere, a point P in σ determines a line OP intersecting the hemisphere, and any line L ⊂ σ determines a plane OL which intersects the hemisphere in half of a great circle . The hemisphere is bounded by a plane through O and parallel to σ. No ordinary line of σ corresponds to this plane; instead

3300-457: The topological plane, which may be thought of as an idealized homotopically trivial infinite rubber sheet, which retains a notion of proximity, but has no distances. The topological plane has a concept of a linear path, but no concept of a straight line. The topological plane, or its equivalent the open disc, is the basic topological neighborhood used to construct surfaces (or 2-manifolds) classified in low-dimensional topology . Isomorphisms of

3375-479: The QR labeling system was applied beyond the automobile industry because of faster reading of the optical image and greater data-storage capacity in applications such as product tracking, item identification, time tracking, document management, and general marketing. The QR code system was invented in 1994, at the Denso Wave automotive products company, in Japan. The initial alternating-square design presented by

3450-459: The QR standard. For example, the generator polynomial used for the Version 1 QR code (21×21), when 7 error correction bytes are used, is: The highest power of x {\displaystyle x} in the polynomial (the degree n {\displaystyle n} , of the polynomial) determines the number of error correction bytes. In this case, the degree is 7. When discussing

3525-575: The Reed–Solomon code phase there is some risk for confusion, in that the QR ISO/IEC standard uses the term codeword for the elements of F 256 {\displaystyle \mathbb {F} _{256}} , which with respect to the Reed–Solomon code are symbols , whereas it uses the term block for what with respect to the Reed–Solomon code are the codewords. The number of data versus error correction bytes within each block depends on (i)

3600-453: The application that scans the QR code retrieves the geo information by using GPS and cell tower triangulation (aGPS) or the URL encoded in the QR code itself is associated with a location. In 2008, a Japanese stonemason announced plans to engrave QR codes on gravestones, allowing visitors to view information about the deceased, and family members to keep track of visits. Psychologist Richard Wiseman

3675-402: The business and using a toll-free number on the website that forwards to the existing line. For websites where the response occurs on the site itself, a site's analytics package can be used to track user behaviour. The process of improving the conversion rate is called conversion rate optimization . However, different sites may consider a "conversion" to be a result other than a sale. Say

3750-583: The capability of accepting payments on the Unified Payments Interface (UPI) platform. QR codes are used in some augmented reality systems to determine the positions of objects in 3-dimensional space. QR codes can be used on various mobile device operating systems. While initially requiring the installation and use of third-party apps, both Android and iOS (since iOS 11 ) devices can now natively scan QR codes, without requiring an external app to be used. The camera app can scan and display

3825-422: The code adds. It is implied by the form of Reed–Solomon used ( systematic BCH view ) that these polynomials are all on the form ∏ i = 0 n − 1 ( x − α i ) {\textstyle \prod _{i=0}^{n-1}(x-\alpha ^{i})} . However, the rules for selecting the degree n {\displaystyle n} are specific to

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3900-458: The complex numbers) complex manifold , sometimes called the complex line . However, this viewpoint contrasts sharply with the case of the plane as a 2-dimensional real manifold. The isomorphisms are all conformal bijections of the complex plane, but the only possibilities are maps that correspond to the composition of a multiplication by a complex number and a translation. In addition, the Euclidean geometry (which has zero curvature everywhere)

3975-450: The corners of the QR code image, using a smaller square (or multiple squares) near the fourth corner to normalize the image for size, orientation, and angle of viewing. The small dots throughout the QR code are then converted to binary numbers and validated with an error-correcting algorithm. The amount of data that can be represented by a QR code symbol depends on the data type ( mode , or input character set), version (1, ..., 40, indicating

4050-413: The customer would maintain a relationship post-sale through support or re-engagement campaigns. Conversion marketing affects all phases of the customer life-cycle, and several conversion marketing solutions are utilized to help ease the transition from one phase to the next. The conversion rate is the proportion of visitors to a website who take action to go beyond a casual content view or website visit, as

4125-489: The elements of which are encoded as bytes of 8 bits ; the byte b 7 b 6 b 5 b 4 b 3 b 2 b 1 b 0 {\displaystyle b_{7}b_{6}b_{5}b_{4}b_{3}b_{2}b_{1}b_{0}} with a standard numerical value ∑ i = 0 7 b i 2 i {\displaystyle \textstyle \sum _{i=0}^{7}b_{i}2^{i}} encodes

4200-410: The encoding of URLs, contact information, and several other data types. The open-source " ZXing " project maintains a list of QR code data types. QR codes have become common in consumer advertising. Typically, a smartphone is used as a QR code scanner, displaying the code and converting it to some useful form (such as a standard URL for a website, thereby obviating the need for a user to type it into

4275-619: The field element ∑ i = 0 7 b i α i {\displaystyle \textstyle \sum _{i=0}^{7}b_{i}\alpha ^{i}} where α ∈ F 256 {\displaystyle \alpha \in \mathbb {F} _{256}} is taken to be a primitive element satisfying α 8 + α 4 + α 3 + α 2 + 1 = 0 {\displaystyle \alpha ^{8}+\alpha ^{4}+\alpha ^{3}+\alpha ^{2}+1=0} . The primitive polynomial

4350-451: The hospitality industry. Restaurants replaced paper or laminated plastic menus with QR code decals on the table, which opened an online version of the menu. This prevented the need to dispose of single-use paper menus, or institute cleaning and sanitizing procedures for permanent menus after each use. Local television stations have also begun to utilize codes on local newscasts to allow viewers quicker access to stories or information involving

4425-402: The image of the QR code. This makes the QR code more secure against counterfeiting attempts; products that display a code which is counterfeit, although valid as a QR code, can be detected by scanning the secure QR code with the appropriate app. The treaty regulating apostilles (documents bearing a seal of authenticity), has been updated to allow the issuance of digital apostilles by countries;

4500-527: The kind of QR code along with the link. These devices support URL redirection , which allows QR codes to send metadata to existing applications on the device. QR codes have been used to establish "virtual stores", where a gallery of product information and QR codes is presented to the customer, e.g. on a train station wall. The customers scan the QR codes, and the products are delivered to their homes. This use started in South Korea , and Argentina, but

4575-494: The need for social distancing during the 2020 COVID-19 pandemic prompted reduced contact between service staff and customers. By specifying the SSID, encryption type, password/passphrase, and if the SSID is hidden or not, mobile device users can quickly scan and join networks without having to manually enter the data. A MeCard -like format is supported by Android and iOS 11+. A QR code can link to an obituary and can be placed on

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4650-431: The opposite direction of abstraction, we may apply a compatible field structure to the geometric plane, giving rise to the complex plane and the major area of complex analysis . The complex field has only two isomorphisms that leave the real line fixed, the identity and conjugation . In the same way as in the real case, the plane may also be viewed as the simplest, one-dimensional (in terms of complex dimension , over

4725-423: The overall dimensions of the symbol, i.e. 4 × version number + 17 dots on each side), and error correction level. The maximum storage capacities occur for version 40 and error correction level L (low), denoted by 40-L: Here are some samples of QR codes: QR codes use Reed–Solomon error correction over the finite field F 256 {\displaystyle \mathbb {F} _{256}} or GF(2) ,

4800-544: The pandemic, including testing and immunization scheduling websites, or for links within stories mentioned in the newscasts overall. In Australia , patrons were required to scan QR codes at shops, clubs, supermarkets, and other service and retail establishments on entry to assist contact tracing . Singapore, Taiwan , the United Kingdom, and New Zealand used similar systems. QR codes are also present on COVID-19 vaccination certificates in places such as Canada and

4875-470: The past 10 years has done little to increase overall conversion rates, so conversion marketing focuses not on driving additional traffic but on converting existing traffic. It requires proactive engagement with consumers using real time analytics to determine if visitors are confused and show signs of abandoning the site; then developing the tools and messages to inform consumers about available products, and ultimately persuading them to convert online. Ideally,

4950-416: The payment system. This allows for various banking apps to facilitate payments between multiple customers and a merchant that displays a single QR code. The SGQR scheme is co-owned by MAS and IMDA. A single SDQR label contains e-payments and combines multiple payment options. People making purchases can scan the code and see which payment options the merchant accepts. QR codes can be used to log into websites:

5025-491: The plane as a 1-dimensional complex manifold , called the complex line . Many fundamental tasks in mathematics, geometry , trigonometry , graph theory , and graphing are performed in a two-dimensional or planar space. In mathematics , a Euclidean plane is a Euclidean space of dimension two , denoted E 2 {\displaystyle {\textbf {E}}^{2}} or E 2 {\displaystyle \mathbb {E} ^{2}} . It

5100-410: The plane can also be given a metric which gives it constant negative curvature giving the hyperbolic plane . The latter possibility finds an application in the theory of special relativity in the simplified case where there are two spatial dimensions and one time dimension. (The hyperbolic plane is a timelike hypersurface in three-dimensional Minkowski space .) The one-point compactification of

5175-473: The plane is homeomorphic to a sphere (see stereographic projection ); the open disk is homeomorphic to a sphere with the "north pole" missing; adding that point completes the (compact) sphere. The result of this compactification is a manifold referred to as the Riemann sphere or the complex projective line . The projection from the Euclidean plane to a sphere without a point is a diffeomorphism and even

5250-522: The team of researchers, headed by Masahiro Hara , was influenced by the black counters and the white counters played on a Go board ; the pattern of the position detection markers was determined by finding the least-used sequence of alternating black-white areas on printed matter, which was found to be (1:1:3:1:1). The functional purpose of the QR code system was to facilitate keeping track of the types and numbers of automobile parts, by replacing individually-scanned bar-code labels on each box of auto parts with

5325-494: The topological plane are all continuous bijections . The topological plane is the natural context for the branch of graph theory that deals with planar graphs , and results such as the four color theorem . The plane may also be viewed as an affine space , whose isomorphisms are combinations of translations and non-singular linear maps. From this viewpoint there are no distances, but collinearity and ratios of distances on any line are preserved. Differential geometry views

5400-491: The user, to open a webpage on the user's device, to add a vCard contact to the user's device, to open a Uniform Resource Identifier (URI), to connect to a wireless network, or to compose an email or text message. There are a great many QR code generators available as software or as online tools that are either free or require a paid subscription. The QR code has become one of the most-used types of two-dimensional code. During June 2011, 14 million American mobile users scanned

5475-400: The version (side length) of the QR symbol and (ii) the error correction level, of which there are four. The higher the error correction level, the less storage capacity. The following table lists the approximate error correction capability at each of the four levels: In larger QR symbols, the message is broken up into several Reed–Solomon code blocks. The block size is chosen so that no attempt

5550-483: Was found that when provided free access to a smartphone with a QR code scanning app, 52.6% of participants would use it to access labelling information. A study made in South Korea showed that consumers appreciate QR code used in food traceability system, as they provide detailed information about food, as well as information that helps them in their purchasing decision. If QR codes are serialised, consumers can access

5625-563: Was one of the first authors to include QR codes in a book, in Paranormality: Why We See What Isn't There (2011). Microsoft Office and LibreOffice have a functionality to insert QR code into documents. QR codes have been incorporated into currency. In June 2011, The Royal Dutch Mint ( Koninklijke Nederlandse Munt ) issued the world's first official coin with a QR code to celebrate the centenary of its current building and premises. The coin can be scanned by

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