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Rectangular Micro QR Code - Wikipedia

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Type of matrix barcode

Rectangular Micro QR Code (rMQR Code) version R17x43

Rectangular Micro QR Code (also known as rMQR Code) is two-dimensional (2D) matrix barcode invented and standardized in 2022[1] by Denso Wave as ISO/IEC 23941.[2] rMQR Code is designed as a rectangular variation of QR code and has the same parameters and applications as original QR code. But rMQR Code is more suitable for the rectangular areas and has difference between width and height up to 19 in R7x139 version. In this way it can be used in places where 1D barcodes are used. rMQR Code can replace Code 128 and Code 39 barcodes with more effective data encoding.

rMQR Code consists of black squares and white square spaces arranged in a square grid on a white background. It has one finder pattern in left-top corner the same as in QR Code and small finder sub-pattern in right-bottom corner. Also, it has alignment and timing patterns to help with recognition. rMQR Code has Reed–Solomon error correction with ability to restore data from corrupted barcodes. As other 2D matrix barcodes it can be read with camera-based readers.

As original QR code, rMQR Code can encode Unicode characters with Extended Channel Interpretation feature, bytes array and can natively encode Japanese characters in kanji encoding. In maximal R17x139 version rMQR Code can encode up to 361 numeric, 219 alphanumeric, 150 bytes and 92 kanji characters.[3]

History and application[edit]

rMQR Code was invented by Denso Wave company in 2022 and standardized as ISO/IEC 23941. It is an extension of QR Code for rectangular areas and designed to be a replacement of 1D barcodes.[4]

rMQR Code is a novel barcode and at this time it not widely used, but it can unite QR Code features like error correction and Unicode encoding and 1D barcodes features like effective usage of rectangular areas. At this time rMQR Code yet is not widely supported by hardware printers and scanners but it is already supported by barcode libraries.[5][6] In this way rMQR Code can be used in:

Main advantages of rMQR Code are:

Rectangular Micro QR Code is designed for the better utilization of rectangular areas with all features of QR code. The symbology consists of black squares and white square spaces arranged in a square grid on a white background. Additionally, the barcode has inverse version with black background with inverse (luminance) color of elements.[2]: 6.2 

rMQR Code has minimal height of 7X and minimal width of 27X, where maximal height is 17X and maximal width 139X.[2]: 7.1  rMQR Code has 32 versions with different combinations of height and width. Reed–Solomon error correction has two levels and allows to restore from 15% to 30% of corrupted data.

Rectangular Micro QR Code (rMQR Code) structure

rMQR Code symbol is constructed from the following elements:[10][2]: 6.3.1 

Here are some samples of Rectangular Micro QR Code (rMQR Code):

Rectangular Micro QR Code can be encoded in 32 versions with height from 7X to 17X and width from 27X to 139X. All versions have two Error correction levels: M and H, which have influence on possible encoded data size and error correction. All of Rectangular Micro QR Code versions and their features can be watched in the following table:[2]: 7.4.10 

Rectangular Micro QR Code (rMQR Code) Versions Version Version
indicator Error
correction
level Data
codewords Error
correction
codewords Data capacity Numeric Alpha Byte Kanji R7x43 0 M 6 7 12 7 5 3 H 3 10 5 3 2 1 R7x59 1 M 12 9 26 16 11 6 H 7 14 14 8 6 3 R7x77 2 M 20 12 45 27 19 11 H 10 22 21 13 9 5 R7x99 3 M 28 16 64 39 27 16 H 14 30 30 18 13 8 R7x139 4 M 44 24 102 62 42 26 H 24 44 54 33 22 14 R9x43 5 M 12 9 26 16 11 6 H 7 14 14 8 6 3 R9x59 6 M 21 12 47 29 20 12 H 11 22 23 14 10 6 R9x77 7 M 31 18 71 43 30 18 H 17 32 37 23 16 9 R9x99 8 M 42 24 97 59 40 25 H 22 44 49 30 20 12 R9x139 9 M 63 36 147 89 61 38 H 33 66 75 46 31 19 R11x27 10 M 7 8 14 8 6 3 H 5 10 9 6 4 2 R11x43 11 M 19 12 42 26 18 11 H 11 20 23 14 10 6 R11x59 12 M 31 16 71 43 30 18 H 15 32 33 20 14 8 R11x77 13 M 43 24 33 20 14 8 H 23 44 52 31 21 13 R11x99 14 M 57 32 133 81 55 34 H 29 60 66 40 27 17 R11x139 15 M 84 48 198 120 82 51 H 42 90 97 59 40 25 R13x27 16 M 12 9 26 16 11 6 H 7 14 14 8 6 3 R13x43 17 M 27 14 62 37 26 16 H 13 28 28 17 12 7 R13x59 18 M 38 22 88 53 36 22 H 20 40 45 27 18 11 R13x77 19 M 53 32 124 75 51 31 H 29 56 66 40 27 17 R13x99 20 M 73 40 171 104 71 44 H 35 78 80 49 33 20 R13x139 21 M 106 60 251 152 104 64 H 54 112 126 76 52 32 R15x43 22 M 33 18 76 46 31 19 H 15 36 33 20 13 8 R15x59 23 M 48 26 112 68 46 28 H 26 48 59 36 24 15 R15x77 24 M 67 36 157 95 65 40 H 31 72 71 43 29 18 R15x99 25 M 88 48 207 126 86 53 H 48 88 111 68 46 28 R15x139 26 M 127 72 301 182 125 77 H 69 130 162 98 67 41 R17x43 27 M 39 22 90 55 37 23 H 21 40 47 28 19 12 R17x59 28 M 56 32 131 79 54 33 H 28 60 63 38 26 16 R17x77 29 M 78 44 183 111 76 47 H 38 84 87 53 36 22 R17x99 30 M 100 60 236 143 98 60 H 56 104 131 79 54 33 R17x139 31 M 152 80 361 219 150 92 H 76 156 178 108 74 46 Finder patter, Finder sub pattern and Corner finder patterns of Rectangular Micro QR Code

Rectangular Micro QR Code has three types of finder pattern:

Main finder pattern is used to detect the barcode on image and its corruption can make barcode unrecognizable.

Finder pattern has vertical and horizontal size 1-1-3-1-1. Finder sub pattern helps to detect bottom-right corner of the barcode. Finder sub pattern does not have guard zone and has vertical and horizontal size 1-1-1-1-1.

Corner finder patterns allows to detect top-right and bottom-left corners and in some version of the rMQR Code can be cut or absent. Corner finder pattern looks like corner with white dot in the center with size 3-3.

Alignment and timing patterns[edit] Alignment and Timing patterns of Rectangular Micro QR Code

Rectangular Micro QR Code has alignment[2]: 6.3.6  and timing patterns[2]: 6.3.5  which help to detect misaligned cells damage. Alignment pattern is represented as black rectangle 3X size rounding 1X white dot. Alignment pattern in some versions can be absent and number of alignment patterns depends from version, up to 8 alignment patterns.

Alignment patterns count Width Alignment patterns count 27 0 43 2 59 4 77 4 99 6 139 8

Timing patterns boarding the barcode where area is clean from finder and alignment patterns and additionally split the barcode vertically in the area of alignment patterns.

Format Information[edit] Format information of Rectangular Micro QR Code

Rectangular Micro QR Code places format information[2]: 7.9  in the area of finder pattern and finder sub pattern. Format information is built as 18-bit sequence containing 6 data bits, 12 error correction bits calculated using the (18, 6) Extended BCH code. Format information is masked with 011111101010110010 sequence which is placed around finder pattern and 100000101001111011 for finder sub pattern.

The first data bit defines error correction level and the second 5 data bits defines version indicator.

Error correction level indicator Error correction level Binary indicator M 0 H 1

Rectangular Micro QR Code uses Reed–Solomon error correction[2]: 7.5  and has two error correction levels M and H which can restore around 15 and 30% of damaged barcode area. All data in the barcode is split into error correction blocks (can be from 1 to 4 blocks) and error correction codewords are added to every block. After this, the blocks are united into single stream.

Error correction levels Error correction level Recovery capacity % M 15% H 30%

rMQR Code use Reed–Solomon error correction over the finite field F 256 {\displaystyle \mathbb {F} _{256}} or GF(28), 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 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 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.

Data masking and placement[edit] Data placement of Rectangular Micro QR Code

Rectangular Micro QR Code places data in the same way as QR code in two-module wide columns[2]: 7.7.3  commencing at the lower right corner of the symbol and running alternately upwards and downwards from the right to the left.

Before the placement the data is masked[2]: 7.8.2  with single type of mask (instead of 8 types in QR Code):
( ( i / 2 ) + ( j / 3 ) ) ( mod 9 ) = 0 {\displaystyle ((i/2)+(j/3)){\pmod {9}}=0} , where
i is a row position;
j is a column position.

Codeword sequence as a single bit stream is placed (starting with the most significant bit) in the two-module wide columns alternately upwards and downwards from the right to left of the symbol. In each column the bits are placed alternately in the right and left modules, moving upwards or downwards according to the direction of placement and skipping areas occupied by function patterns, changing direction at the top or bottom of the column. Each bit shall always be placed in the first available module position.

When the data capacity of the symbol is such that it does not divide exactly into a number of 8-bit symbol characters, the appropriate number of remainder bits (1 to 7) shall be used to fill the symbol capacity. These remainder bits shall always have the value 0 before data masking.

Rectangular Micro QR Code can encode 361 numeric, 219 alphanumeric, 150 bytes and 92 kanji characters[11] in the maximal version R17x139. Additionally, it allows to encode Unicode data with Extended Channel Interpretation feature and encode GS1 data.[9]

rMQR Code can encode data in 8 modes[2]: 7.4.1  where 4 modes are data encoding modes and 3 modes are indicator modes, like ECI. Also, every encoding sequence must be completed with special Terminator mode.

Mode and Mode indicators for rMQR Mode Mode indicators (3 bits) Numeric 001 Alphanumeric 010 Byte 011 Kanji 100 FNC1 101 (First position) 110 (Second position) ECI 111 Terminator
(End of message) 000

rMQR Code usually encodes data in mixed mode[2]: 7.4.7  which is a combination of existing modes for better compactification or special selectors like ECI designator.

rMQR Mixed mode encoding Segment 1 ECI header 1 Segment 2 Segment 3 Terminator Mode 1 Data count Data ECI Mode 1 ECI designator Mode 2 Data count Data Mode 3 Data count Data

Every compaction mode depends on version[2]: 7.4.1  to select number of bits which are used as encoded characters (numbers, letters, bytes) counter. The number of bits required for every version can be watched in the following table.

Number of bits of character count indicator Version Numeric
mode Alpha
mode Byte
mode Kanji
mode Version Numeric
mode Alpha
mode Byte
mode Kanji
mode R7x43 4 3 3 2 R13x27 5 5 4 3 R7x59 5 5 4 3 R13x43 6 6 5 5 R7x77 6 5 5 4 R13x59 7 6 6 5 R7x99 7 6 5 5 R13x77 7 7 6 6 R7x139 7 6 6 5 R13x99 8 7 7 6 R9x43 5 5 4 3 R13x139 8 8 7 7 R9x59 6 5 5 4 R15x43 7 6 6 5 R9x77 7 6 5 5 R15x59 7 7 6 5 R9x99 7 6 6 5 R15x77 8 7 7 6 R9x139 8 7 6 6 R15x99 8 7 7 6 R11x27 4 4 3 2 R15x139 9 8 7 7 R11x43 6 5 5 4 R17x43 7 6 6 5 R11x59 7 6 5 5 R17x59 8 7 6 6 R11x77 7 6 6 5 R17x77 8 7 7 6 R11x99 8 7 6 6 R17x99 8 8 7 6 R11x139 8 7 7 6 R17x139 9 8 8 7

Rectangular Micro QR Code encodes digits 0–9 in numeric mode.[2]: 7.4.3  The number sequence is split into 3 digits which converted to 10 bits (000 - 999). Last 2 and 1 numbers are encoded in 7 and 4 bits. rMQR Code in numeric mode encodes 001 as mode indicator, then numbers counter and then numbers sequence converted into bits.

Numeric mode encoding Numbers count Bits count Value Bits 3 10 734 1011011110 3 10 001 0000000001 2 7 72 1001000 1 4 5 00101

Rectangular Micro QR Code encodes 2 alphanumeric characters[2]: 7.4.4  from the table into 11 bits stream with the following formula:
V = 45 ∗ C 1 + C 2 {\displaystyle V=45*C_{1}+C_{2}}

Encoding/decoding table for alphanumeric mode Value Character Value Character Value Character Value Character Value Character 0 0 9 9 18 I 27 R 36 Space 1 1 10 A 19 J 28 S 37 $ 2 2 11 B 20 K 29 T 38 % 3 3 12 C 21 L 30 U 39 * 4 4 13 D 22 M 31 V 40 + 5 5 14 E 23 N 32 W 41 - 6 6 15 F 24 O 33 X 42 . 7 7 16 G 25 P 34 Y 43 / 8 8 17 H 26 Q 35 Z 44 :

Final character is encoded into 6 bits. rMQR Code in alphanumeric mode encodes 010 as mode indicator, then alphanumeric counter and then bits stream which represents encoded characters.

Rectangular Micro QR Code adds mode indicator 011 and bytes counter (version dependent) before the byte stream,[2]: 7.4.5  converted into 8-bit sequence.

Rectangular Micro QR Code encodes characters from 2 bytes JIS X 0208 2-byte character set[2]: 7.4.6  into 13 bits with the following rules:

  1. subtract 0x8140 from Shift JIS value;
  2. multiply most significant byte of result by 0xC0;
  3. add least significant byte to product from step 2;
  4. convert result to a 13-bit binary string.
  1. subtract 0xC140 from Shift JIS value;
  2. multiply most significant byte of result by 0xC0;
  3. add least significant byte to product from step 2;
  4. convert result to a 13-bit binary string.

rMQR Code adds mode indicator 100 and characters counter before the encoded kanji sequence.

Unicode encoding with ECI[edit]

Rectangular Micro QR Code encodes Unicode characters with Extended Channel Interpretation.[2]: 7.4.2.2  Previously it encodes ECI designator which defines encoding charset. After this, it encodes byte array of Unicode characters encoded into byte stream with mix of numeric-text-byte modes. The default ECI designator is \000003(ISO/IEC 8859-1).

ECI designator is encoded with mode indicator 111 and ECI assignment number which can be encoded in 8, 16 or 24 bits by rules from the following table.

Encoding ECI assignment number ECI assignment value Codewords count Codeword values 000000 to 000127 1 0bbbbbbb 000000 to 016383 2 10bbbbbb bbbbbbbb 000000 to 999999 3 110bbbbb bbbbbbbb bbbbbbbb where b ... b is the binary value of the ECI Assignment number

Rectangular Micro QR Code can encode GS1 Data with FNC1 in first position.[2]: 7.4.8.2  Encoding mode indicator 101 switch the barcode symbol in GS1 Application Identifiers[9] mode. FNC1 cannot be used as split FNC1 character like in Code 128 symbol. Instead of this, % character should be used in alphanumeric mode or GS (0x1D) in byte mode. To encode % character in alphanumeric mode the character should be doubled %% and after decoding it should be transmitted as single % character.

FNC1 in second position[edit]

FNC1 in second position[2]: 7.4.8.3  at this time has historical value and is not used. It was used to encode (obsolete at this time) mode identifier as first data codeword in Code 128 when FNC1 character is encoded in the second codeword (second position). More detail description you can read in ISO/IEC 15417[12] Annex B.

Rectangular Micro QR Code encodes FNC1 in second position as mode indicator 111, 8-bit application identifier (AIM, but I am not sure) and any other mode/modes after this.

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