Data Matrix

A Data Matrix is a two-dimensional code consisting of black and white "cells" or dots arranged in either a square or rectangular pattern, also known as a matrix. The information to be encoded can be text or numeric data. The usual data size is from a few bytes up to 1556 bytes. 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 2,335 alphanumeric characters.
Data Matrix symbols are rectangular, usually square in shape and composed of square "cells" which represent bits. 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 and two other borders consisting of alternating dark and light "cells" or modules. 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 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.

Applications

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 and the fact that the code can be read with only a 20% contrast ratio.
A Data Matrix is scalable; commercial applications exist with images as small as and as large as a 1-metre square. Fidelity of the marking and reading systems are the only limitation.
The US Electronic Industries Alliance recommends using Data Matrix for labeling small electronic components.
Data Matrix codes are becoming common on printed media such as labels and letters. The code can be read quickly by a barcode 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. 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, 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.

Food industry

Data Matrix codes are used in the food industry in autocoding 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.

Art

In May 2006 a German computer programmer, Bernd Hopfengärtner, created a large Data Matrix in a wheat field. The message read "Hello, World!".

Technical specifications

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 entire ASCII character set. 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.

Data Matrix ECC 200

ECC 200, the newer version of Data Matrix, uses Reed–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.
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. All symbols using the ECC 200 error correction can be recognized by the upper-right corner module being the same as the background color..
Additional capabilities that differentiate ECC 200 symbols from the earlier standards include:

Inverse reading symbols
Specification of the character set
Rectangular symbols
Structured append
Data Matrix ECC 000–140

Older versions of Data Matrix include ECC 000, ECC 050, ECC 080, ECC 100, ECC 140. Instead of using Reed–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 a cyclic redundancy check 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..
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."

Standards

Data Matrix was invented by International Data Matrix, Inc. which was merged into RVSI/Acuity CiMatrix, who were acquired by Siemens AG in October 2005, Microscan Systems in September 2008, and Omron in 2017. Data Matrix is covered today by several ISO/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
ISO/IEC 15415—2-D Print quality standard
ISO/IEC 15418:2016—Symbol data format semantics
ISO/IEC 15424:2008—Data Carrier Identifiers
ISO/IEC 15434:2006—Syntax for high-capacity ADC media
ISO/IEC 15459—Unique identifiers
Error correction

Data Matrix codes use Reed–Solomon error correction over the finite field , the elements of which are encoded as bytes of 8 bits; the byte with a standard numerical value encodes the field element where is taken to be a primitive element satisfying. The primitive polynomial is, corresponding to the polynomial number 301, with initial root = 1 to obtain generator polynomials. The Reed–Solomon code uses different generator polynomials over, 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:,
which gives:
or with decimal coefficients:

Encoding

The encoding process is described in the ISO/IEC standard 16022:2006. Open-source software for encoding and decoding the ECC-200 variant of Data Matrix has been published.
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, the padding and error correction bytes, and four modules of unused space.
The symbol is of size 16×16, with 12 data bytes and 12 error correction bytes. A Reed Solomon code shortened to 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 code, is:
which may also be written in the form of a matrix of decimal coefficients:
'
The 12-byte long message "Wikipedia" including 'End', P1 and P2, in decimal coefficients, is:
'
Using the procedure for Reed-Solomon systematic encoding, the 12 error correction bytes obtained in the form of the remainder after polynomial division are:
'
These error correction bytes are then appended to the original message. The resulting coded message has 24 bytes, and is in the form:
'
or in decimal coefficients:
'
and in hexadecimal coefficients:
'
Multiple encoding modes are used to store different kinds of messages. The default mode stores one ASCII character per 8-bit codeword. Control codes are provided to switch between modes, as shown below.

Codeword	Codeword hexadecimal	Interpretation
0	0	Not used
1–128	1-80	ASCII data
129	81	End of message
130–229	82-e5	Digit pairs 00–99
230	e6	Begin [\|C40] encoding
231	e7	Begin [\|Base 256] encoding
232	e8	FNC1
233	e9	Structured append. Allows a message to be split across multiple symbols.
234	ea	Reader programming
235	eb	Set high bit of the following character
236	ec	05 Macro
237	ed	06 Macro
238	ee	Begin ANSI X12 encoding
239	ef	Begin [\|Text] encoding
240	f0	Begin EDIFACT encoding
241	f1	Extended Channel Interpretation code
242–255	f2-ff	Not used