AData Matrix is atwo-dimensional code consisting of black and white "cells" or dots arranged in either asquare orrectangular pattern, also known as amatrix. The information to be encoded can be text or numeric data. The usual data size is from a few bytes up to 1556bytes. The length of the encoded data depends on the number of cells in the matrix.Error correction codes are often used to increase reliability: even if one or more cells are damaged so it is unreadable, the message can still be read. A Data Matrix symbol can store up to 2,335alphanumeric characters.

Data Matrix symbols are rectangular, usually square in shape and composed of square "cells" which representbits. Depending on the coding used, a "light" cell represents a 0 and a "dark" cell is a 1, or vice versa. Every Data Matrix is composed of two solid adjacent borders in an "L" shape (called the "finder pattern") and two other borders consisting of alternating dark and light "cells" or modules (called the "timing pattern"). Within these borders are rows and columns of cells encoding information. The finder pattern is used to locate and orient the symbol while the timing pattern provides a count of the number of rows and columns in the symbol. As more data is encoded in the symbol, the number of cells (rows and columns) increases. Each code is unique. Symbol sizes vary from 10×10 to 144×144 in the new version ECC 200, and from 9×9 to 49×49 in the old version ECC 000 – 140.

The most popular application for Data Matrix is marking small items, due to the code's ability to encode fifty characters in a symbol that is readable at 2 or 3 mm² (0.003 or 0.005 sq in) and the fact that the code can be read with only a 20% contrast ratio.^[1]A Data Matrix is scalable; commercial applications exist with images as small as 300 micrometres (0.012 in) (laser etched on a 600-micrometre (0.024 in) silicon device) and as large as a 1-metre (3 ft) square (painted on the roof of aboxcar). Fidelity of the marking and reading systems are the only limitation.The USElectronic Industries Alliance (EIA) recommends using Data Matrix for labeling small electronic components.^[2]

Data Matrix codes are becoming common on printed media such as labels and letters. The code can be read quickly by abarcode reader which allows the media to be tracked, for example when a parcel has been dispatched to the recipient.

For industrial engineering purposes, Data Matrix codes can be marked directly onto components, ensuring that only the intended component is identified with the data-matrix-encoded data. The codes can be marked onto components with various methods, but within the aerospace industry these are commonly industrial ink-jet, dot-peen marking, laser marking, and electrolytic chemical etching (ECE). These methods give a permanent mark which can last up to the lifetime of the component.

Once marked onto the component, reader cameras along the production line, as well as camera used by technicians after production is complete, can decode the Data Matrix to read relevant information. This can include the date of manufacture, serial number, and any other relevant information the manufacturer chooses to include. These reader cameras can also be used to track the movement of the component through the production line, as well as performing inventory stock checks.

Data Matrix codes, along with other open-source codes such as 1D barcodes can also be read with mobile phones by downloading code specific mobile applications. Although many mobile devices are able to read 2D codes including Data Matrix Code,^[3] few extend the decoding to enable mobile access and interaction, whereupon the codes can be used securely and across media; for example, in track and trace, anti-counterfeit, e.govt, and banking solutions.

Data Matrix codes are used in thefood industry inautocoding systems to prevent food products being packaged and dated incorrectly. Codes are maintained internally on a food manufacturers database and associated with each unique product, e.g. ingredient variations. For each product run the unique code is supplied to the printer. Label artwork is required to allow the 2D Data Matrix to be positioned for optimal scanning. For black on white codes testing isn't required unless print quality is an issue, but all color variations need to be tested before production to ensure they are readable.^{[citation needed]}

In May 2006 a German computer programmer, Bernd Hopfengärtner, created a large Data Matrix in a wheat field (in a fashion similar tocrop circles). The message read "Hello, World!".^[4]

Data Matrix symbols are made up of modules arranged within a perimeter finder and timing pattern. It can encode up to 3,116 characters from the entireASCII character set (with extensions). The symbol consists of data regions which contain modules set out in a regular array. Large symbols contain several regions. Each data region is delimited by a finder pattern, and this is surrounded on all four sides by a quiet zone border (margin). (Note: The modules may be round or square- no specific shape is defined in the standard. For example, dot-peened cells are generally round.)

ECC 200, the newer version of Data Matrix, usesReed–Solomon codes for error and erasure recovery. ECC 200 allows the routine reconstruction of the entire encoded data string when the symbol has sustained 30% damage, assuming the matrix can still be accurately located. Data Matrix has an error rate of less than 1 in 10 million characters scanned.^[5]

Symbols have an even number of rows and an even number of columns. Most of the symbols are square with sizes from 10 × 10 to 144 × 144. Some symbols however are rectangular with sizes from 8×18 to 16×48 (even values only). All symbols using the ECC 200 error correction can be recognized by the upper-right corner module being the same as the background color. (binary 0).

Additional capabilities that differentiate ECC 200 symbols from the earlier standards include:

• Inverse reading symbols (light images on a dark background)
• Specification of the character set (viaExtended Channel Interpretations)
• Rectangular symbols
• Structured append (linking of up to 16 symbols to encode larger amounts of data)

^[6]

Older versions of Data Matrix include ECC 000, ECC 050, ECC 080, ECC 100, ECC 140. Instead of usingReed–Solomon codes like ECC 200, ECC 000–140 use a convolution-based error correction. Each varies in the amount of error correction it offers, with ECC 000 offering none, and ECC 140 offering the greatest. For error detection at decode time, even in the case of ECC 000, each of these versions also encode acyclic redundancy check (CRC) on the bit pattern. As an added measure, the placement of each bit in the code is determined by bit-placement tables included in the specification. These older versions always have an odd number of modules, and can be made in sizes ranging from 9 × 9 to 49 × 49. All symbols utilizing the ECC 000 through 140 error correction can be recognized by the upper-right corner module being the inverse of the background color. (binary 1).

According to ISO/IEC 16022, "ECC 000–140 should only be used in closed applications where a single party controls both the production and reading of the symbols and is responsible for overall system performance."

Data Matrix was invented byInternational Data Matrix, Inc. (ID Matrix) which was merged into RVSI/Acuity CiMatrix, who were acquired bySiemens AG in October 2005, Microscan Systems in September 2008, and Omron in 2017. Data Matrix is covered today by severalISO/IEC standards and is in the public domain for many applications, which means it can be used free of any licensing or royalties.

• ISO/IEC 16022:2024—Data Matrix bar code symbology specification^[7]
• ISO/IEC 15415—2-D Print quality standard
• ISO/IEC 15418:2016—Symbol data format semantics (GS1 application identifiers and ASC MH10 data identifiers and maintenance)
• ISO/IEC 15424:2008—Data Carrier Identifiers (including Symbology Identifiers) [IDs for distinguishing different barcode types]
• ISO/IEC 15434:2006—Syntax for high-capacity ADC media (format of data transferred from scanner to software, etc.)
• ISO/IEC 15459—Unique identifiers

Data Matrix codes useReed–Solomon error correction over thefinite field${\displaystyle {\mathbb{F}}_{256}}$ (orGF(2⁸)), the elements of which are encoded asbytes of 8 bits; the byte${\displaystyle b_7{b}_6{b}_5{b}_4{b}_3{b}_2{b}_1{b}_0}$ with a standard numerical value${\displaystyle \sum _{i=0}^7{b}_i{2}^i}$ encodes the field element${\displaystyle \sum _{i=0}^7{b}_i{\alpha }^i}$ where${\displaystyle \alpha \in {\mathbb{F}}_{256}}$ is taken to be a primitive element satisfying${\displaystyle {\alpha }^8+{\alpha }^5+{\alpha }^3+{\alpha }^2+1=0}$. The primitive polynomial is${\displaystyle x^8+x^5+x^3+x^2+1}$, corresponding to the polynomial number 301, with initial root = 1 to obtain generator polynomials. The Reed–Solomon code uses different generator polynomials over${\displaystyle {\mathbb{F}}_{256}}$, depending on how many error correction bytes the code adds. The number of bytes added is equal to the degree of the generator polynomial.

For example, in the 10 × 10 symbol, there are 3 data bytes and 5 error correction bytes. The generator polynomial is obtained as:${\displaystyle g(x)=(x+\alpha )(x+{\alpha }^2)(x+{\alpha }^3)(x+{\alpha }^4)(x+{\alpha }^5)}$,

which gives:${\displaystyle g(x)=x^5+{\alpha }^{235}{x}^4+{\alpha }^{207}{x}^3+{\alpha }^{210}{x}^2+{\alpha }^{244}x+{\alpha }^{15}}$,

or with decimal coefficients:${\displaystyle g(x)=x^5+62x^4+111x^3+15x^2+48x+228}$.

The encoding process is described in theISO/IEC standard 16022:2006.^[8] Open-source software for encoding and decoding the ECC-200 variant of Data Matrix has been published.^[9][10]

The diagrams below illustrate the placement of the message data within a Data Matrix symbol. The message is "Wikipedia", and it is arranged in a somewhat complicated diagonal pattern starting near the upper-left corner. Some characters are split in two pieces, such as the initial W, and the third 'i' is in "corner pattern 2" rather than the usual L-shaped arrangement. Also shown are the end-of-message code (marked End), the padding (P) and error correction (E) bytes, and four modules of unused space (X).

The symbol is of size 16×16 (14×14 data area), with 12 data bytes (including 'End' and padding) and 12 error correction bytes. A (255,243,6) Reed Solomon code shortened to (24,12,6) is used. It can correct up to 6 byte errors or erasures.

To obtain the error correction bytes, the following procedure may be carried out:

The generator polynomial specified for the (24,12,6) code, is:${\displaystyle g(x)=x^{12}+242x^{11}+100x^{10}+178x^9+97x^8+213x^7+142x^6+42x^5+61x^4+91x^3+158x^2+153x+41}$,which may also be written in the form of a matrix of decimal coefficients:

[1 242 100 178 97 213 142 42 61 91 158 153 41]

The 12-byte long message "Wikipedia" including 'End', P1 and P2, in decimal coefficients (see the diagrams below for the computation method using ASCII values), is:

[88 106 108 106 113 102 101 106 98 129 251 147]

Using the procedure forReed-Solomon systematic encoding, the 12 error correction bytes obtained (E1 through E12 in decimal) in the form of the remainder after polynomial division are:

[104 216 88 39 233 202 71 217 26 92 25 232]

These error correction bytes are then appended to the original message. The resulting coded message has 24 bytes, and is in the form:

[W i k i p e d i a 'End' P1 P2E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11 E12]

or in decimal coefficients:

[88 106 108 106 113 102 101 106 98 129 251 147104 216 88 39 233 202 71 217 26 92 25 232]

and in hexadecimal coefficients:

[58 6A 6C 6A 71 66 65 6A 62 81 FB 9368 D8 58 27 E9 CA 47 D9 1A 5C 19 E8]

Multiple encoding modes are used to store different kinds of messages. The default mode stores oneASCII character per 8-bit codeword. Control codes are provided to switch between modes, as shown below.

The C40, Text andX12 modes are potentially more compact for storing text messages. They are similar toDEC Radix-50, using character codes in the range 0–39, and three of these codes are combined to make a number up to 40³=64000, which is packed into two bytes (maximum value 65536) as follows:

V = C1×1600 + C2×40 + C3 + 1

B1 = floor(V/256)

B2 = V mod 256

The resulting value of B1 is in the range 0–250. The special value 254 is used to return to ASCII encoding mode.

Character code interpretations are shown in the table below. The C40 and Text modes have four separate sets. Set 0 is the default, and contains codes that temporarily select a different set for the next character. The only difference is that they reverse upper-and lower-case letters. C40 is primarily upper-case, with lower-case letters in set 3; Text is the other way around. Set 1, containing ASCII control codes, and set 2, containing punctuation symbols are identical in C40 and Text mode.

EDIFACT mode uses six bits per character, with four characters packed into three bytes. It can store digits, upper-case letters, and many punctuation marks, but has no support for lower-case letters.

Base 256 mode data starts with a length indicator, followed by a number of data bytes. A length of 1 to 249 is encoded as a single byte,and longer lengths are stored as two bytes.

L1 = floor(length / 250) + 249, L2 = length mod 250

It is desirable to avoid long strings of zeros in the coded message, because they become large blank areas in the Data Matrix symbol, which maycause a scanner to lose synchronization. (The default ASCII encoding does not use zero for this reason.) In order to make that less likely, thelength and data bytes are obscured by adding a pseudorandom value R(n), where n is the position in the byte stream.

R(n) = (149 × n) mod 255 + 1

Prior to the expiration of US patent 5,612,524^[11] in November 2007, intellectual property companyAcacia Technologies claimed that Data Matrix was partially covered by its contents. As the patent owner, Acacia allegedly contacted Data Matrix users demanding license fees related to the patent.

Cognex Corporation, a large manufacturer of 2D barcode devices, filed adeclaratory judgment complaint on 13 March 2006 after receiving information that Acacia had contacted its customers demanding licensing fees. On 19 May 2008 Judge Joan N. Ericksen of the U.S. District Court in Minnesota ruled in favor of Cognex.^[12] The ruling held that the '524 patent, which claimed to cover a system for capturing and reading 2D symbology codes, is both invalid and unenforceable due toinequitable conduct by the defendants during the procurement of the patent.

While the ruling was delivered after the patent expired, it precluded claims for infringement based on use of Data Matrix prior to November 2007.

A German patent application DE 4107020 was filed in 1991, and published in 1992. This patent is not cited in the above US patent applications and might invalidate them.^{[citation needed]}

• PDF417
• Aztec Code
• High Capacity Color Barcode
• MaxiCode
• Nintendo e-Reader
• QR Code
• Semacode
• SPARQCode
• Trusted paper key

Wikimedia Commons has media related toDataMatrix.

• GS1 DataMatrix Guideline: Overview and technical introduction to the use of GS1 DataMatrix
• Datamatrix Code Generator - Online Tool

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