View source for Rectangular Micro QR Code

{{Short description|Type of matrix barcode}}
[[File:Rectangular Micro QR Code Example R17x43.svg|thumb|Rectangular Micro QR Code (rMQR Code) version R17x43]]
'''Rectangular Micro QR Code''' (also known as '''rMQR Code''') is [[Barcode#Matrix (2D) codes|two-dimensional (2D) matrix barcode]]  invented and standardized in 2022<ref>{{cite news |url=https://www.rfid-wiot-search.com/denso-new-mobile-computer-bht-m70-and-rmqr-code-launched-on-the-market |title=New Mobile Computer BHT-M70 and rMQR Code Launched on the Market |newspaper=Rfid & Wireless Iot |date=2022}}</ref> by [[Denso#Denso Wave|Denso Wave]] as ISO/IEC 23941.<ref name="iso23941">{{cite web |author=ISO/IEC |url=https://www.iso.org/standard/77404.html |id=ISO/IEC 23941 |title=ISO/IEC 23941:2022 "Information technology Automatic identification and data capture techniques Rectangular Micro QR Code (rMQR) bar code symbology specification" |website=iso.org |publisher=[[International Organization for Standardization|International Organization for Standardization(ISO)]] |date=2022}}</ref> 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 [[Barcode reader#Camera-based readers|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 [[JIS X 0208|kanji]] encoding. In maximal R17x139 version rMQR Code can encode up to 361 numeric, 219 alphanumeric, 150 bytes and 92 kanji characters.<ref>{{cite web |url=https://japantoday.com/category/tech/qr-codes-evolve-into-their-newest-form-a-bar-qr-code |title=QR codes evolve into their newest form: a bar QR code |website=japantoday.com |date=2022}}</ref>

==History and application==

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 [[Universal Product Code|1D barcodes]].<ref>{{cite web |url=https://www.denso-wave.com/en/adcd/info/detail__220525.html |title=DENSO WAVE Develops "rMQR Code", a new rectangular QR Code that can even be printed in long, narrow spaces |website=www.denso-wave.com}}</ref>

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.<ref>{{cite web |url=https://github.com/OUDON/rmqrcode-python |title=Rectangular Micro QR Code (rMQR Code) Generator |website=github.com}}</ref><ref>{{cite web |url=https://docs.aspose.com/barcode/net/qr-micro-qr-and-rmqr/ |title=Generate QR Code, Micro QR Code and Rectangular Micro QR Code in C# |website=aspose.com}}</ref> In this way rMQR Code can be used in:
* [[Advertising|Advertisement]];
* Automatic data identification in [[document processing]];
* Automatically identified [[hyperlinks]] to internet pages;
* [[Grocery store|Food and goods tracking]] in retail;
* In airports, bus / railroad stations for automatic tickets and passenger documents identification;
* [[Package tracking]];<ref>{{cite web |url=https://ascii.jp/elem/000/004/092/4092570/ |title=細長いQRコード「rMQRコード」登場。狭いスペースに印字可能(Introducing the elongated QR code "rMQR code". Can print in narrow spaces)  |website=ascii.jp |language=Japanese}}</ref>
* Patient or medicine identification in healthcare services or industry.<ref>{{cite web |url=https://www.hibcc.org/wp-content/uploads/ANSI-HIBC-1.3-FINAL_errata.pdf#page=30 |title=ANSI HIBC 1.3 Provider Applications Standard |website=www.hibcc.org |publisher=The Health Industry Business Communications Council |page=30 |date=2010}}</ref>

Main advantages of rMQR Code are:
* Ability to encode Japanese characters with embedded methods;
* Effective usage of rectangular areas and full replacement of 1D barcodes.
* Encoding [[GS1]] Data;<ref name="gs1ai">{{cite web |url=https://ref.gs1.org/ai/ |title=GS1 Application Identifiers |website=www.gs1.org}}</ref>
* [[Extended Channel Interpretation]] support;
* [[Reed–Solomon error correction]] with ability to restore data from corrupted barcodes.

==Barcode design==
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 ([[Grayscale#Colorimetric (perceptual luminance-preserving) conversion to grayscale|luminance]]) color of elements.<ref name="iso23941"/>{{rp|6.2}}

rMQR Code has minimal height of 7X and minimal width of 27X, where maximal height is 17X and maximal width 139X.<ref name="iso23941"/>{{rp|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.

[[File:Rectangular Micro QR Code Structure.png|thumb|Rectangular Micro QR Code (rMQR Code) structure]]

rMQR Code symbol is constructed from the following elements:<ref>{{cite web |url=https://www.qrcode.com/en/codes/rmqr.html |title=QR Code: rMQR Code |website=www.qrcode.com}}</ref><ref name="iso23941"/>{{rp|6.3.1}}
* Finder pattern on top-left corner with 1X separator on bottom-right space, the same as in QR Code;
* Finder sub pattern in bottom-right corner;
* Corner finder patterns on top-right and bottom-left barcode sides, width and height variable and maximal can be 3x3;
* Alignment patterns, variable count, depends from version width: 0 in R11x27 version, 8 in R11x139 version;
* Timing patterns which are used as border around barcode;
* Format information region around finder pattern and finder sub pattern;
* Data encoding region;
* Quiet zone 2X.

Here are some samples of Rectangular Micro QR Code (rMQR Code): 
<gallery widths="220" heights="220">
File:Rectangular Micro QR Code Example R7x43.svg|Rectangular Micro QR Code (rMQR Code) version R7x43
File:Rectangular Micro QR Code Example R17x43.svg|Rectangular Micro QR Code (rMQR Code) version R17x43
File:Rectangular Micro QR Code Example R7x139.svg|Rectangular Micro QR Code (rMQR Code) version R7x139
File:Rectangular Micro QR Code Example R17x139.svg|Rectangular Micro QR Code (rMQR Code) version R17x139
File:Rectangular Micro QR Code Example R11x77.svg|Rectangular Micro QR Code (rMQR Code) version R11x77
File:Rectangular Micro QR Code Example R15x59.svg|Rectangular Micro QR Code (rMQR Code) version R15x59
</gallery>

===Versions===
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:<ref name="iso23941"/>{{rp|7.4.10}}

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

===Finder patterns===
[[File:Rectangular Micro QR Code Finder Corner Patterns.png|thumb|Finder patter, Finder sub pattern and Corner finder patterns of Rectangular Micro QR Code]]

Rectangular Micro QR Code has three types of finder pattern:
* Finder pattern<ref name="iso23941"/>{{rp|6.3.3}} on top-left corner with 1X separator on bottom-right space;
* Finder sub pattern<ref name="iso23941"/>{{rp|6.3.7}} in bottom-right corner;
* Possible corner finder patterns<ref name="iso23941"/>{{rp|6.3.8}} on top-right and bottom-left barcode corners.

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===
[[File:Rectangular Micro QR Code Alignment Timing Pattrens.png|thumb|Alignment and Timing patterns of Rectangular Micro QR Code]]
Rectangular Micro QR Code has alignment<ref name="iso23941"/>{{rp|6.3.6}} and timing patterns<ref name="iso23941"/>{{rp|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.

{| class="wikitable" border="1" style="text-align:center"
|+ 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===
[[File:Rectangular Micro QR Code Format Information.png|thumb|Format information of Rectangular Micro QR Code]]
Rectangular Micro QR Code places format information<ref name="iso23941"/>{{rp|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.

{| class="wikitable" border="1" style="text-align:center"
|+ Rectangular Micro QR Code (rMQR Code) Format information bits
|-
!Error <br>correction<br> level
!colspan=5|Version indicator
!colspan=12|Error correction bits
|-
|<math>X_0</math>||<math>X_1</math>||<math>X_2</math>||<math>X_3</math>||<math>X_4</math>||<math>X_5</math>||<math>X_6</math>||<math>X_7</math>||<math>X_8</math>||<math>X_9</math>||<math>X_{10}</math>||<math>X_{11}</math>||<math>X_{12}</math>||<math>X_{13}</math>||<math>X_{14}</math>||<math>X_{15}</math>||<math>X_{16}</math>||<math>X_{17}</math>
|}

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

{| class="wikitable" border="1" style="text-align:center"
|+ Error correction level indicator
|-
!Error correction level
!Binary indicator
|-
|M||0
|-
|H||1
|}

===Error correction===
Rectangular Micro QR Code uses [[Reed–Solomon error correction]]<ref name="iso23941"/>{{rp|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.

{| class="wikitable" border="1" style="text-align:center"
|+ Error correction levels
|-
!Error correction level
!Recovery capacity %
|-
|M||15%
|-
|H||30%
|}

rMQR Code use [[Reed–Solomon error correction]] over the [[finite field]] <math>\mathbb{F}_{256}</math> or {{math|GF(2<sup>8</sup>)}}, the elements of which are encoded as [[Octet (computing)|bytes of 8 bits]]; the byte <math>b_7b_6b_5b_4b_3b_2b_1b_0</math> with a standard numerical value <math>\textstyle\sum_{i=0}^7 b_i 2^i</math> encodes the field element <math>\textstyle\sum_{i=0}^7 b_i \alpha^i</math> where <math> \alpha \in \mathbb{F}_{256}</math> is taken to be a primitive element satisfying <math>\alpha^8 + \alpha^4 + \alpha^3 + \alpha^2 + 1 = 0</math>. The primitive polynomial is <math>x^8 + x^4 + x^3 + x^2 + 1 </math>, corresponding to the polynomial number 285, with initial root = 0.

===Data masking and placement===
[[File:Rectangular Micro QR Code Data Placement.png|thumb|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<ref name="iso23941"/>{{rp|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<ref name="iso23941"/>{{rp|7.8.2}} with single type of mask (instead of [[QR code#Encoding|8 types in QR Code]]):
<br><math>((i / 2) + (j / 3) )\pmod{9} = 0</math>, where 
<br>'''i''' is a row position;
<br>'''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.

==Encoding==

Rectangular Micro QR Code can encode 361 numeric, 219 alphanumeric, 150 bytes and 92 [[JIS X 0208|kanji]] characters<ref>{{cite web |url=https://barcodeguide.seagullscientific.com/Content/Symbologies/rMQRCode.htm |title=barcodeguide.seagullscientific.com: rMQR Code |website=barcodeguide.seagullscientific.com}}</ref> in the maximal version R17x139. Additionally, it allows to encode Unicode data with Extended Channel Interpretation feature and encode [[GS1]] data.<ref name="gs1ai"/>

rMQR Code can encode data in 8 modes<ref name="iso23941"/>{{rp|7.4.1}} where 4 modes are data encoding modes and 3 modes are indicator modes, like [[Extended Channel Interpretation|ECI]]. Also, every encoding sequence must be completed with special Terminator mode.

{| class="wikitable" border="1" style="text-align:center"
|+ Mode and Mode indicators for rMQR
|-
!Mode
!Mode indicators (3 bits)
|-
|Numeric||001
|-
|Alphanumeric||010
|-
|Byte||011
|-
|Kanji||100
|-
|rowspan = 2|FNC1||101 (First position)
|-
|110 (Second position)
|-
|ECI||111
|-
|Terminator<br>(End of message)||000
|}
rMQR Code usually encodes data in mixed mode<ref name="iso23941"/>{{rp|7.4.7}} which is a combination of existing modes for better compactification or special selectors like ECI designator.

{| class="wikitable" border="1" style="text-align:center"
|+ rMQR Mixed mode encoding
|-
!colspan = 3|Segment 1
!colspan = 2|ECI header 1
!colspan = 3|Segment 2
!colspan = 3|Segment 3
!rowspan = 2|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<ref name="iso23941"/>{{rp|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.

{| class="wikitable" border="1" style="text-align:center"
|+ Number of bits of character count indicator
|-
!Version
!Numeric <br>mode
!Alpha <br>mode
!Byte <br>mode
!Kanji <br>mode
!Version
!Numeric <br>mode
!Alpha <br>mode
!Byte <br>mode
!Kanji <br>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
|}

===Numeric mode===
Rectangular Micro QR Code encodes digits 0–9 in numeric mode.<ref name="iso23941"/>{{rp|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.

{| class="wikitable" border="1" style="text-align:center"
|+ 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
|}

===Alphanumeric mode===
Rectangular Micro QR Code encodes 2 alphanumeric characters<ref name="iso23941"/>{{rp|7.4.4}} from the table into 11 bits stream with the following formula:
<br><math>V = 45 * C_1 + C_2</math>

{| class="wikitable" border="1" style="text-align:center"
|+ 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.

===Byte mode===
Rectangular Micro QR Code adds mode indicator '''011''' and bytes counter (version dependent) before the byte stream,<ref name="iso23941"/>{{rp|7.4.5}} converted into 8-bit sequence.

===Kanji mode===
Rectangular Micro QR Code encodes characters from 2 bytes [[JIS X 0208]] 2-byte character set<ref name="iso23941"/>{{rp|7.4.6}} into 13 bits with the following rules:
* For characters with Shift JIS values from 0x8140 to 0x9FFC:
# subtract 0x8140 from Shift JIS value;
# multiply most significant byte of result by 0xC0;
# add least significant byte to product from step 2;
# convert result to a 13-bit binary string.
* For characters with Shift JIS values from 0xE040 to 0xEBBF:
# subtract 0xC140 from Shift JIS value;
# multiply most significant byte of result by 0xC0;
# add least significant byte to product from step 2;
# 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===

Rectangular Micro QR Code encodes Unicode characters with Extended Channel Interpretation.<ref name="iso23941"/>{{rp|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 [[ISO/IEC 8859-1|\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.

{| class="wikitable" border="1" style="text-align:center"
|+ 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
|-
|colspan = 3|where b ... b is the binary value of the ECI Assignment number
|}

===GS1 encoding===
Rectangular Micro QR Code can encode GS1 Data with FNC1 in first position.<ref name="iso23941"/>{{rp|7.4.8.2}} Encoding mode indicator '''101''' switch the barcode symbol in GS1 Application Identifiers<ref name="gs1ai"/> 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===
FNC1 in second position<ref name="iso23941"/>{{rp|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<ref name="iso15417">{{cite web |author=ISO/IEC |url=https://www.iso.org/standard/43896.html |id=ISO/IEC 15417 |title=ISO/IEC 15417:2007 "Information technology Automatic identification and data capture techniques Code 128 bar code symbology specification" |website=iso.org |publisher=[[International Organization for Standardization|International Organization for Standardization(ISO)]] |date=2007}}</ref> 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.

==See also==
* [[Automated identification and data capture]] (AIDC)
* [[Barcode]]
* [[Denso#Denso Wave|Denso Wave]]
* [[Extended Channel Interpretation]]
* [[QR code]]

==References==
{{reflist|32em}}

==External links==
* [https://products.aspose.app/barcode/generate/qr?type=rectmicroqr Free Rectangular Micro QR Code generator]
* [https://products.aspose.app/barcode/recognize Free Rectangular Micro QR Code reader]
* [https://www.qrcode.com/en/codes/rmqr.html Rectangular Micro QR Code description]

{{Barcodes}}
{{ISO standards}}

[[Category:Automatic identification and data capture]]
[[Category:Barcodes]]
[[Category:Encodings]]
[[Category:Japanese inventions]]