The MATRIX suite of codes

Julian Rose
23-27 December, 2001

This page is a tribute to my father, Geoffrey John Rose, M.A. (Cantab), 1934-2001. It describes the MATRIX suite of barcode designs that he developed.

Copyright Notices:  This page is Copyright (C) 2001, Julian Rose, Sussex U.K.  The MATRIX design is Copyright (C) 1985-1994, Geoffrey  Rose, Sussex, U.K. Certain MATRIX application copyrights or other commercial interests may also be held by limited company.

Notices:

  1. Anyone is free to apply the code designs described herein, but the designs may neither be modified nor extended without prior written permission from this author who is acting in the capacity of copyright guardian. To put it another way, MATRIX is copyrighted and is neither public domain nor Open Source nor otherwise licensed.
  2. Commercial hardware is available to scan the codes (requiring PC or terminal keyboard, or serial host interfaces, and a pen or scanner reader) and reference software (for 32-bit MS-Windows) is available to reproduce them.

1. Overview

MATRIX is a suite of several related barcodes providing full alphanumeric and mixed international alphabet support, at the same time providing good space efficiency, safety and legibility. The symbology can be auto-descriminated safely in the presence of the major symbologies, at the same time offering a range of features which exceed those available with existing symbologies. These include:
  1. Segregation of text, decoder hardware configuration and other domains
  2. Capability of representing all alphabets and accents in a single barcode
  3. Representation of all keys on a keyboard
  4. Built-in future expansion potential

1.1 General description

MATRIX is a binary 1-dimensional code symbology, with wide & narrow modulation of both bars and gaps. The suite comprises 10 related codes, where each member occupies a different functional domain. The MATRIX format is quite conventional, comprising:

1.1.1 Start and stop patterns

There are twelve 3-bar & 3-gap patterns used for end codes. Their formats enable bi-directional reading. Ten of the patterns are used as START codes, one for each of the member barcodes. One START code [MAT C, 0x12] also serves as the forwards STOP code common to each member, which leaves the remaining two end patterns as the reverse STOP codes. [The forwards direction refers to input scanning left-to-right.]

1.1.2 Check pattern

The CHECK pattern is constructed using a selected algorithm which possesses a check generator value for all data bars and gaps in any barcode. The check generator value is different for each of the ten members of the suite [see Appendix A1]. The check is applied to the barcode pattern, not to the characters represented; this supports the concept of a pattern domain distinct from the character domain.
1.1.2.1 worked checksum at read time
[Let
    N be a narrow bar, value 0
    W be a wide bar, value 1
    n be a narrow gap, value 0
    w be a wide gap, value 1]

Consider the example barcode [written notationally]:
    NnWwNnWwNnNnNwNnWwWwWnNnWwN[n]

The START (3 bars, 3 gaps) is binary 010010 or 0x12, so this is MAT C [refer to Appendix A1]. The check generator is 0xB5 (10110101 binary), and there are 4 bars and 4 gaps per character.
a. Set out the data [underlined] and check bits [italic] in sequence
b. From the left, ignore all lead 0s and the next 1
c. EXCLUSIVE OR the next 8 bits with the check generator
d. repeat from b. until 8 bits are left. A zero result is OK.

The following division illustrates the above worked checksum example:
1 0 0 0 1 0 0 1 0 1 1 1 0 1 1 0
1 0 1 1 0 1 0 1
1 0 1 0 0 1 1 1 1
1 0 1 1 0 1 0 1
1 1 1 1 1 0 1 0 1
1 0 1 1 0 1 0 1
0 1 0 0 0 0 0 0 1 0
1 0 1 1 0 1 0 1
1 0 1 1 0 1 1 1 1
1 0 1 1 0 1 0 1
1 1 0 1 1 0 1 0 1
1 0 1 1 0 1 0 1
0 0 0 0 0 0 0 0 0

1.1.2.2 worked checksum at print time
Consider the example when the text EEC is required as a barcode. Character analysis defines that MAT 1 is required. The START pattern 0x09 (3 bars, 3 gaps) will be used. The character count is odd, so a leading zero will be inserted. The check generator value is 0xE5.
a. Set out the data in character sequence. Append 8 zero bits.
b. From the left, ignore all lead 0s and the next 1
c. EXCLUSIVE OR the next 8 bits with the check generator
d. Repeat from b. above until 8 bits remain. This is the check pattern.

The following division illustrates the above worked checksum example:
0 0 0 0 1 1 1 0 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0
1 1 1 0 0 1 0 1
0 0 1 1 1 0 0 0 1 0 0
1 1 1 0 0 1 0 1
0 0 1 0 0 0 0 1 0 0 0
1 1 1 0 0 1 0 1
1 1 1 0 1 1 0 1 0
1 1 1 0 0 1 0 1
0 0 1 1 1 1 1 1 0 0 0
1 1 1 0 0 1 0 1
0 0 0 1 1 1 0 1 0
Print out the MAT 1 START pattern (0x09) as 3 bars interleaved 3 gaps, the data as 4 bars alternately 4 gaps (0EEC), the CHECK pattern first 4 bits as bars, the last 4 bits as gaps, and lastly append the STOP pattern (0x12) as 3 bars interleaved 3 gaps:
    NnNnWwNwNwNwNnWwWwWnNnNwNnWwWnNnWwN[n]

1.2 Suite member identification

Each member is recognised by having a unique START pattern and also a unique check generator value. These two parameters give satisfactory member identification. The ten members are assigned the identies:

2. MATs 1 through 4

These four codes, colloquially the 'normal' codes, have functions closely related to the popular barcode symbologies. They carry alphanumeric text strings. The quantity of text characters in a given barcode string is, within reason, unlimited. Each character is represented by a group of bars, alternatively by a group of gaps. The quantity of bars & gaps used for a character depends upon which of the four codes is in use. No data character uses both bars and gaps, unlike the START, STOP and CHECK patterns.

For each of the normal codes the first character is represented in the first bar pattern following the START pattern, the second character in the first gap pattern, the third character in the second bar pattern, etc. Thus an even quantity of characters is forced. At print time, if an odd quantity of characters is submitted then the string has a zero (MAT 1) or space (MATs 2-4) inserted in front. At read time, a decoder can be conditioned to process the lead insertion character as required, using character count controls.

The choice of which normal MAT code to use is made at print time. The submitted character string is first reviewed and the most junior, i.e. space-economical, code capable of representing every submitted character is selected. The choice is totally transparent to the user who need never be aware of the selected code unless undertaking manual analysis.

2.1 MAT 1

This uses 4-bit binary data groups to represent characters. With 16 possible data patterns, the 16 characters which can be represented are 0 to 9 and A to F.

2.2 MAT 2

This uses 6-bit binary data groups, giving 64 data patterns. MAT 2 represents characters in the mid-section of the lower ASCII table from space to underscore. The set of MAT 1 characters is a subset of those representable in MAT 2.

2.3 MAT 3

This uses 7-bit binary data groups, giving 128 patterns. MAT 3 represents the full lower ASCII table range of characters. The set of MAT 2 characters is a subset of those represented by MAT 3.

2.4 MAT 4

This uses 8-bit binary data groups, giving 256 data patterns. The extra data space, beyond the capacity of the full lower ASCII table representable in MAT 3, is used to represent a range of characters selected from the several alternative upper tables. This includes accented Latin characters and alternative alphabets. Eight codes are reserved for within-string controls, of which seven have yet to be assigned functions. These controls are reserved, so can never be confused with text. [See appendix B.] The set of MAT 3 characters is a subset of those represented by MAT 4.

3. Other MATRIX suite members

'Popular' barcodes, like the MATRIX 'normal' codes, carry text strings. Clearly there is a requirement to represent other function domains, such as decoder setup and control. Most decoder manufacturers nominate selected text barcodes to use as control commands. This intersection of text domain with control domain is problematic and can add user complexity. By incorporating distinct domain representation usage can be easier, and user problems can be reduced.

The function domains that have been identified as meaningful to represent separately, and the corresponding MATRIX codes are:

For now MATs J and K remain to be assigned. Even more members of the MATRIX family could be added if necessary, by sub-function expansion of MAT J and K.

3.1 MAT C

MAT C data occupies only 4 bars and the 4 interleaved gaps, so providing 256 data patterns (or 8-bit binary data groups), to represent the decoder control domain. A decoder setup & control document can have up to 256 unique barcodes which do not intersect the text or any other domain. A decoder manufacturer may define the use made to control their range of decoders.

3.1.1 Pattern assignments

MAT C is used exclusively for decoder set-up and control. Each barcode pattern represents a single 8-bit control value, i.e. decimal 0 through 255 (0x0 through 0xFF). Each value is assigned a function required in controlling the decoder rather than in conveying text.

The 8 bits are packed into 4 bars and 4 gaps in the barcode data region. The bars contain the most significant half [nibble] of the value (most significant bit first [left-to-right]) and the gaps contain the least significant half [nibble]. Each MAT C barcode therefore will always contain 14 bars and 13 gaps, to accomodate START, data, CHECK and STOP patterns.

3.2 MAT D

MAT D data also occupies 4 bars and 4 gaps, so providing 256 unique data patterns (or 8-bit binary data groups). These are taken to be equivalent to the data pattern domain used in MAT 3 and MAT 4 table 0. Thus codes can be printed which represent individual characters. The functional advantage of creating this data domain is that MAT D is independent of any automatic prefix & suffix & append processing or code enable & disable controls selected for normal data strings.

3.2.1 Pattern assignments

MAT D is used exclusively for single character representation. The barcode pattern contains an 8-bit value, i.e. decimal 0 through 255 (0x0 through 0xFF). Each value corresponds to a single character as used in MAT 4 lower table, or upper table zero [see appendix B]. This allows for the construction of single character pages as transient inputs, which will not undergo decoder processing selected for normal [text] strings.

The 8 bits are packed into 4 bars and 4 gaps in the barcode data region. the bars contain the most significant half [nibble] of the value (most significant bit first [left-to-right]) and the gaps contain the least significant half. Each MAT D barcode therefore will always contain 14 bars and 13 gaps, to accomodate START, data, CHECK and STOP patterns.

3.3 MAT G

[Information on MAT G is scant, but appears to be as follows.] If MAT G data space is limited to 4 bars and 4 gaps, then 256 unique data patterns can be used to represent the alphanumeric control keyboard domain. If one considers the 'regular' alphanumeric etc. keys on a keyboard, it is possible to identify no more than 64 keys. Representing each together with either CTRL or ALT makes a total of 128 codes; if SHIFT is also represented together with CTRL or ALT then a further 128 codes are added to make a total of 256 codes.  To put it another way, MAT G might be considered to consist of the MAT 3 codes with either CTRL or ALT applied to represent a single character.

3.3.1 Pattern assignments

MAT G is used exclusively for keyboard control key representation. The barcode pattern contains an 8-bit value, i.e. 0 through 255 (0x0 through 0xFF). Each value is assigned to the alphanumeric keys with either CTRL or ALT applied.

The 8 bits are packed into 4 bars and 4 gaps in the barcode data region. The bars contain the most significant half [nibble] of the value (most significant bit first [left-to-right]) and the gaps contain the least significant half. Each MAT G barcode therefore will always contain 14 bars and 13 gaps, to accomodate START, data, CHECK and STOP patterns.

3.4 MAT H

MAT H data space is likewise limited to 4 bars and 4 gaps, so providing 256 unique data patterns (or 8-bit binary data groups). These are used to represent 'peripheral' keys on a keyboard - function keys, numeric pad, non-ASCII control keys, etc. Most keyboards don't exceed a key count of 123. If one discounts the 'regular' alphanumeric etc. keys and considers only the numeric keypad, cursor controls and function keys, it is usually possible to identify no more than 64 extra keys. Thus the MAT H structure can represent 64 keys, each with or without SHIFT or ALT making a total of 256 codes.

To illustrate the potential benefit of MAT H, representation of programmable function keys by barcode could allow the printing of a function key barcode document. Such a document could serve in keyboard-unfriendly environments for example.

3.4.1 Pattern assignments

MAT H is used exclusively for keyboard total key representation. The barcode pattern contains an 8-bit value, i.e. 0 through 255 (0x0 through 0xFF). Each value is assigned to keys on, and selected by reference to published pages of standard keyboard layouts.

The 8 bits are packed into 4 bars and 4 gaps in the barcode data region. The bars contain the most significant half [nibble] of the value (most significant bit first [left-to-right]) and the gaps contain the least significant half. Each MAT H barcode therefore will always contain 14 bars and 13 gaps, to accomodate START, data, CHECK and STOP patterns.

[Diagrams exist to] show various keyboard layouts [122-keys, 84-keys and 88-keys], and the assignment of values to those keys for which no ASCII table is published. [It would be possible to produce] extra diagrams, one for each keyboard layout that users may encounter. Apart from some dedicated equipments and novelties, the range of keyboard layouts is reasonably limited, largely due to the influence of major suppliers like IBM and DEC.

4. General design consideration

The MATRIX design began to be developed in the mid-1980's, resulting from reservations about aspects of the available symbologies, also awareness of the limitations of ASCII compared with then emerging equipment design. As a result MATRIX offers a range of features which both exceeds what is avaailable with existing standard symbologies and optimises usage.

4.0.1 External factors, safety and legibility

External factors are those beyond the control of the symbology design which influence achievement of the specification. Such features include:
    print quality & accuracy
    print contrast, reflectivity or spectral effects
    input device sensitivity and spectral response
    print damage
The total effect of variations in these factors is to cause the perceived widths or counts of bars and gaps to deviate from the specification ideal.

SAFETY may be defined as the ability correctly to reject out-of-specification print examples. LEGIBILITY may be defined as the ability correctly to accept in-specification print examples in the presence of eroding external influences. A barcode design should have sufficient features to achieve adequate safety, at the same time not so many features that it undermines user requirements such as print space economy and legibility.
 
Feature For Against 1 2 3 4 5 6 7 8 9
Start/stop complexity Improves late entry/early exit detection Print space inefficiency + + + + - - + - +
Redundant data patterns Multiple error rejection opportunities Print space inefficiency + + - + - - - + -
Uniform space per character Multiple error rejection opportunities Print space inefficiency - + + + + + + + -
Check pattern Total data pattern validation Print space inefficiency - - + + + + + - +
Multi-width data patterns Alternative form of redundant patterns Reduced legibility tolerance. Analogue not digital approach. - - + + + - - - -
Decoder character count checks Total pattern validation. Compensates for inadequate total pattern features n/a / / / / / / / / /
The above table uses the code identities:
    1. Codabar
    2. Code 39
    3. Code 93
    4. Code 128
    5. EAN or UPC or JAN
    6. MSI
    7. Plessey
    8. 2 of 5 codes
    9. Matrix

4.1 Error detection and elimination

Due to insufficient checks, some of the popular barcodes are inadequately safe in error detection & elimination. This is particularly so where different character counts must co-exist. The inadequacy can be demonstrated by scanning a newspaper page using a poorly set-up decoder; spurious decodes can be observed. The MATRIX suite was designed to include a total pattern CHECK character which copes with several problems including mixed character counts and some aspects of inadequate set-up. This is enhanced by incorporating an adequate START & STOP pattern structure, which copes with late-entry and early-exit problems.

4.2 Binary versus multi-width codes

An analysis follows of why binary codes make less demands on printing technology than multi-width codes. This is particularly significant in multi-part printing. MATRIX is therefore a binary symbology. Ratio 3:1 binary codes are potentially more legible than multi-width codes. Consider should a multi-width design, like Code 128 for example, be printed using inadequate equipment so being out of specification; this could potentially cause customers delay and cost, which has in fact been known to happen. A binary code would give less problems considering the print methods used.

4.2.1 Barcode tolerances

Ideally all printed barcodes have no perceivable perturbations on the edges between bars and gaps. The ideal is unachievable, but some print techniques produce better edge quality than others, often at a cost. The user frequently finds out the hard way that barcode technology is not trivial.

It is suggested that there are only four types of print error:

  1. a black spot in a gap
  2. a white spot in a bar
  3. a black spot intersecting an edge
  4. a white spot intersecting an edge
Any one printed barcode may suffer from several examples of these simultaneously. It is useful to eveluate the effect of a single error. Cases 1 and 2 would generate wrong counts of bars & gaps which would therefore lead to rejection. They need no further evaluation. Cases 3 and 4 are essentially identical. Consider an adjacent bar and gap with one wider than the other. Consider an edge error where the wider element is reduced in width, and the narrower element increased in width, by the error. Consider this for both binary and multi-width barcodes.

Let:
    unity be the width of the narrowest bar & gap
    &mu be the wide to narrow ratio for a binary code
    &theta be the wide element width in a multi-width code
    &phi be the narrow element width in a multi-width code
    &delta be the error width

4.2.1.1 multi-width codes
Bars and gaps are ideally 1, 2, 3 or 4 units wide. The error changes the perceived wide element width from &theta to (&theta-&delta). The narrow element perceived width changes from &phi to (&phi+&delta). An error boundary arises when &delta becomes as large as 0.5, because the element then appear to be one unity width different from the correct values. The multi-width error to no-error boundary value for &delta is 0.5.
4.2.1.2 binary codes
The error causes the narrow element width to change from unity to (1+&delta). At the same time the wide element width changes from &mu to (&mu-&delta). An error boundary condition occurs when the wide and narrow elements become the same width, i.e. when (1+&delta)=(&mu-&delta). It is then indeterminate which is the wide and which is the narrow element. Thus the binary error to no-error boundary value is when &delta=0.5(&mu-1).
4.2.1.3 conclusion
If &mu=2 then &delta=0.5, the same as for multi-width codes. If &mu=3 then &delta=1.0. Therefore a binary code printed with a wide to narrow ratio of 2:1 has the same error tolerance as a multi-width code. A binary code printed with a ration of 3:1 is twice as tolerant to errors as a multi-width code.

4.3 Print space economy

Some users have print-space limitations. MATRIX deliberately avoids the use of redundant character patterns while remaining succesfully legible. As a result, for numeric strings MATRIX generally provides good print-space economy compared with other binary codes, while also enforcing use of a check pattern. Some other binary codes don't use a check, so need to rely on the setting of a character count or redundant patterns for safety. For alphanumeric strings MATRIX (2:1 wide to narrow ratio) is more economic than the 3 standard codes [Code 39, Code 93, Code 128]. Code 128 alone gives better economy than MATRIX 3:1 but not MATRIX 2:1; Code 128 is however multi-width, therefore is only equal to MATRIX 2:1 in legibility.

4.4 ASCII, keyboards and barcodes

The popular barcodes were built around the ASCII table. These codes were created to represent the text string domain, and until the early-1990's were limited to subsets of the lower ASCII table. However the table, while mostly necessary, has fallen behind sufficiency; a glance at the keytops on modern international keyboards illustrates this point. While it is feasible to redeploy selected character strings to achieve extended representations, there is a risk, rare but not unknown, of accidental mapping from one functional domain into another.

If it can be considered the original design of the 'popular' barcodes [for the lower ASCII text string domain] is limiting and the risks and costs associated with customisation [into other domains] inhibit some users and applications, then it might also be considered the expansion of barcode application has been held back. These considerations suggest that it would be beneficial to establish barcodes capable of carrying data beyond the scope of the lower ASCII table, and beyond the text string domain. MATs 4, C, D, G and H are one result.

4.5 Accented characters

In 1994, MATRIX was the only code offering accented characters until the publication of the Code 128 planned revision making use of FNC4. A comparison of techniques is illuminating.

4.5.1 Code 128

[As of May 1994.] The proposal is for Code 128 to represent characters beyond the lower ASCII table using FNC4. A printed barcode will optionally use FNC4 attached to any selected lower ASCII table character to transform it, thus representing an upper table character. The resulting upper table character has a table & value position 128 greater than the thus-transformed lower table character.

Unfortunately, there is more than one upper ASCII table. Different tables are published which assign different values to a given character, also different characters to a given table. Because the value rather than the character is generated, the Code 128 proposed technique is unsafe to use outside a closed application. In practice different equipments and software use different tables, and these can need to co-exist in a large communicating complex or international organisation.

Prior to this Code 128 proposal, any barcode string printed using this symbology could be relied upon to represent the same characters no matter where in the world it was sent, and in what equipment it was used. This proposal will for the first time produce barcodes which will no longer be portable. If such codes are transported then character conversions will happen without warning or easy traceability, but within the design of the symbology. It has to be suggested this Code 128 proposal is seriously flawed.

4.5.2 MAT 4

MAT 4 offers a safe method of representing upper table characters. A given character is assigned a unique value, nothing to do with ASCII. The printed barcode always has the same pattern for the character and the same character for the pattern. When the code is read the character is recognised in the decoder, which can then map it via the local host equipment look-up table to the correct local host transmission protocol. Thus extended character tables are universal, and barcodes containing their characters will remain totally portable. Appendix B gives the values already assigned to a range of characters.

4.6 MATRIX expansion

The 'popular' barcodes offer little if any expansion potential. This is certainly not the case with the MATRIX suite, which already goes beyond the functionality of most, if not all, other code designs, and still has plenty of room for manoeuvre while preserving safety.

It is feasible to assign extra functions to the MAT 4 within-code controls, also to select extra extended start codes and checksum generators, and so provide even more expansion potential. It is reasonable to suggest that these extensions would allow simultaneous non-intersecting representation of Arabic, Cryllic, Greek, Hebrew, Kanji and others. [As of May 1994] such representation is already claimed for the Code 128 development, but safety and character table interference have been glossed over. With MAT 4 it will be possible to identify further function domains and support them without domain intersection.

[One aim remains to submit MATRIX to a standardisation process, so management of it and expansion would be  effected under the aegis of a controlling body.]

Appendix A - character patterns MATs 1-4 (lower half)

A1. General

Each barcode pattern represents a series of text characters selected from the lower ASCII table. The character string forms the data content of the printed barcode. The data section of the barcode pattern is preceded by a start pattern and followed by a check pattern and stop pattern. The following table gives the control parameters for each member of the MATRIX suite.
 
MATRIX identity START pattern Character bits CHECK generator Character count
1 0x09 4 0xE5 unlimited i.e. string
2 0x11 6 0xD5 unlimited
3 0x0A 7 0xCB unlimited
4 0x16 8 0xB1 unlimited
C 0x12 8 0xB5 1 i.e. singleton
D 0x0C 8 0xAD 1
G 0x0E TBA [8] 0xA3 1
H 0x0D 8 0x9D 1
J 0x13 TBA 0xF3 TBA
K 0x0B TBA 0xCF TBA
Ths STOP pattern is 0x12. The reverse STOP is either 0x14 or 0x15.

Each character is represented by a value which can be given in decimal, hexadecimal or binary form. The binary format is directly converted to the barcode printed pattern, with each binary bit represented. A binary 1 is shown as a wide and a binary 0 as narrow. As many bits are used per character as defined for the Matrix barcode being considered, i.e. 4 bits for MAT 1, 6 bits for MAT 2, 7 bits for MAT 3 and 8 bits for MAT 4. If necessary, leading binary 0 bits are inserted in each character binary pattern to make the defined quantity of bits for the barcode [i.e. padding].

Each character pattern is printed either totally in a series of bars, alternatively totally in a series of gaps. In a string of characters:
    the first character is represented in the bars pattern following the START pattern,
    the second character is represented in the gaps pattern, interleaved with the first character bars,
    the third character is in the next bars group,
    the fourth character is in the gaps, interleaved with the third character,
and so on. Thus all characters in odd positions are represented in the bars while all even position characters are represented in the gaps. At print time, if an odd quantity of characters is submitted, then a 0 (MAT 1) or SPACE (MATs 2, 3 and 4) is inserted at the beginning to force an even character count, prior to identifying the even and odd character positions.

A2. MAT 1 character patterns

The values and characters used in MAT 1 are as follows:
 
ASCII character Barcode decimal Barcode hex Barcode binary Barcode pattern
0 0 0x0 0000 NNNN
1 1 0x1 0001 NNNW
2 2 0x2 0010 NNWN
3 3 0x3 0011 NNWW
4 4 0x4 0100 NWNN
5 5 0x5 0101 NWNW
6 6 0x6 0110 NWWN
7 7 0x7 0111 NWWW
8 8 0x8 1000 WNNN
9 9 0x9 1001 WNNW
A 10 0xA 1010 WNWN
B 11 0xB 1011 WNWW
C 12 0xC 1100 WWNN
D 13 0xD 1101 WWNW
E 14 0xE 1110 WWWN
F 15 0xF 1111 WWWW

A3. MAT 2 character patterns

MAT 2 patterns use 6 binary bits, which provide 64 unique patterns. The 64 characters so represented are taken from the lower ASCII table, [starting] from SPACE (32 or 0x20) to UNDERSCORE (95 or 0x5F) consecutively. The decimal or hexadecimal or binary value used for MAT 2 representation of a character is obtained by selecting the ASCII table value and subtracting 32 (0x20). Because of this simple relationship, only a few characters need be illustrated as examples:
 
ASCII character ASCII decimal Barcode decimal Barcode hex Barcode binary Barcode pattern
SPACE 32 0 0x0 000000 NNNNNN
& 38 6 0x6 000110 NNNWWN
0 48 16 0x10 010000 NWNNNN
A 65 33 0x21 100001 WNNNNW
Z 90 58 0x3A 111010 WWWNWN
UNDERSCORE 95 63 0x3F 111111 WWWWWW

A4. MAT 3 character patterns

MAT 3 patterns use 7 binary bits, so providing 128 unique patterns. The characters represented are those in the full lower ASCII table. The decimal or hexadecimal or binary value used for MAT 3 representation of a character is obtained by selecting the ASCII table value. Because of this simple relationship, only a few characters are shown here as examples:
 
ASCII character ASCII decimal Barcode hexadecimal Barcode binary Barcode pattern
NULL 0 0x0 0000000 NNNNNNN
& 38 0x26 0100110 NWNNWWN
0 48 0x30 0110000 NWWNNNN
A 65 0x41 1000001 WNNNNNW
Z 90 0x5A 1011010 WNWWNWN
UNDERSCORE 95 0x5F 1011111 WNWWWWW
a 97 0x61 1100001 WWNNNNW
z 122 0x7A 1111010 WWWWNWN
TILDE 126 0x7E 1111110 WWWWWWN

A5. MAT 4 (lower half) character patterns

MAT 4 patterns use 8 binary bits, so providing 256 unique patterns. The characters represented by the lower half exactly match those represented by MAT 3. Only a few characters are shown here as examples:
 
ASCII character ASCII decimal Barcode hexadecimal Barcode binary Barcode pattern
NULL 0 0x0 00000000 NNNNNNNN
& 38 0x26 00100110 NNWNNWWN
0 48 0x30 00110000 NNWWNNNN
A 65 0x41 01000001 NWNNNNNW
Z 90 0x5A 01011010 NWNWWNWN
UNDERSCORE 95 0x5F 01011111 NWNWWWWW
a 97 0x61 01100001 NWWNNNNW
z 122 0x7A 01111010 NWWWWNWN
TILDE 126 0x7E 01111110 NWWWWWWN

Appendix B - MAT 4 (upper half) pattern assignments

MAT 4 (upper half) uses character values in the range 128 to 255. Because the upper tables of MAT 4 are defined only for MAT 4, any value can safely be assigned to a text character or to an upper table control function.

B1. Within-code controls

The following 8 values (common to all upper tables) are reserved for within-code controls, for decoder function management: 128, 144, 160, 176, 192, 208, 224 and 240.

The value 128 (0x80) has been assigned as a table change control. This will allow for several alternative upper tables, e.g. Arabic, Cryllic, Greek, Hebrew, Kanji and others to co-exist. It will allow for within-code switching between tables. The switch is achieved by submitting the value 128 followed by a table identifier value i.e. a 2-byte control. Identifier zero is assigned to the accented Latin table given below; other identifiers are yet to be assigned. Table zero is the default table.

B2. Table zero

The following assignments have been made to MAT 4 table zero:
 
A E I O U Y a e i o u y
Acute 129 130 131 132 133 134 193 194 195 196 197 198
Tilde 135 136 137 138 139 140 199 200 201 202 203 204
Grave 145 146 147 148 149 150 209 210 211 212 213 214
Circumflex 161 162 163 164 165 166 225 226 227 228 229 230
Umlaut 177 178 179 180 181 182 241 242 243 244 245 246
MAT 4 table zero - main accented Latin characters
A further sixteen assignments are made to represent other accented Latin characters. [These are illustrated in the following table using lower ASCII approximations:]
 
Ao ao AE ae O o C? c? N~ n~ cent pound para ss Pt )o(
141 205 142 206 143 207 158 222 159 223 189 174 175 237 238 239
MAT 4 table zero - additional accented Latin characters
The table zero assignments, plus the 8 controls, use 84 of the 128 available codes. Therefore 44 more assignments can be added before MAT 4 table zero is full up. These can be assigned as users identify their barcode needs.

B3. MAT 4 expansion

Other upper tables can be defined as users identify their needs. [It has been suggested that upper tables might be defined to support other alphabets e.g. Arabic, Cryllic, Greek, Hebrew, Kanji. This would need careful analysis.]

[Notes

  1. It might also be considered how MAT J and K can be defined usefully. Many alphabets are identified by the unicode consortium and can be found at http://www.unicode.org/charts/. This would seem to fit the purpose of MATRIX. Perhaps MAT J can be defined like MAT D to carry 16 character bits with 1 character count which would support unicode characters or singletons. Alternatively, it might be defined like MAT 4 to carry 16 character bits with unlimited character count which would support unicode strings. This too needs careful consideration and should follow unicode standardisation much like ASCII standardisation is already followed.
  2. Expansion would also require suitable decoder setup and control support within MAT C. Perhaps MAT C may be modified, along the lines of MAT H, where within-code functions would allow the selection of alternative upper-table control pages. The aim is to support common settings but also allow for different decoder private capability settings.
  3. It might be prudent to leave MAT K reserved; beyond this member count unique START patterns might become exhausted.
]

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