Rectangular Micro QR Code

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:^{[2]: 7.4.10}

Finder patterns

Rectangular Micro QR Code has three types of finder pattern:

• Finder pattern^[2]: 6.3.3 on top-left corner with 1X separator on bottom-right space;
• Finder sub pattern^[2]: 6.3.7 in bottom-right corner;
• Possible corner finder patterns^[2]: 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

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.

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

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.

Rectangular Micro QR Code (rMQR Code) Format information bits

Error correction level	Version indicator					Error correction bits
${\displaystyle X_{0}}$	${\displaystyle X_{1}}$	${\displaystyle X_{2}}$	${\displaystyle X_{3}}$	${\displaystyle X_{4}}$	${\displaystyle X_{5}}$	${\displaystyle X_{6}}$	${\displaystyle X_{7}}$	${\displaystyle X_{8}}$	${\displaystyle X_{9}}$	${\displaystyle X_{10}}$	${\displaystyle X_{11}}$	${\displaystyle X_{12}}$	${\displaystyle X_{13}}$	${\displaystyle X_{14}}$	${\displaystyle X_{15}}$	${\displaystyle X_{16}}$	${\displaystyle X_{17}}$

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

Error correction

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.

rMQR Code use Reed–Solomon error correction over the finite field ${\displaystyle \mathbb {F} _{256}}$ or GF(2⁸), the elements of which are encoded as bytes 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 ${\displaystyle \textstyle \sum _{i=0}^{7}b_{i}2^{i}}$ encodes the field element ${\displaystyle \textstyle \sum _{i=0}^{7}b_{i}\alpha ^{i}}$ where ${\displaystyle \alpha \in \mathbb {F} _{256}}$ is taken to be a primitive element satisfying ${\displaystyle \alpha ^{8}+\alpha ^{4}+\alpha ^{3}+\alpha ^{2}+1=0}$. The primitive polynomial is ${\displaystyle x^{8}+x^{4}+x^{3}+x^{2}+1}$, corresponding to the polynomial number 285, with initial root = 0.

Data masking and placement

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):
${\displaystyle ((i/2)+(j/3)){\pmod {9}}=0}$, 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.

Numeric mode

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.

Alphanumeric mode

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

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,^[2]: 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^[2]: 7.4.6 into 13 bits with the following rules:

• For characters with Shift JIS values from 0x8140 to 0x9FFC:

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.

• For characters with Shift JIS values from 0xE040 to 0xEBBF:

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

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.

GS1 encoding

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

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.