QR Generator

Inside the matrix

How a QR Code is assembled and read

A QR Code is not a square of arbitrary pixels. Fixed landmarks orient the scanner; metadata explains how to decode it; a zigzag stream carries segment headers, payload, padding and Reed-Solomon recovery data.

Open the generator Follow the bitstream
Real Version 7 matrix, colored by the same categories used in Debug > Overlay.
Finder Alignment Timing Format EC level Mask Version Mode Character count Data Terminator Padding EC words Remainder

01 / Anatomy

Landmarks tell a scanner where the grid is

Functional patterns are reserved before the encoded stream is placed. They are not payload bytes, and the data traversal steps around them.

Finder patterns

Three 7-by-7 targets identify the symbol and its rotation. A one-module light separator isolates each target from nearby modules.

Alignment patterns

Version 2 and higher add smaller 5-by-5 targets. Their number grows with the version so a reader can correct perspective and surface distortion.

Timing tracks

Alternating dark and light modules on row 6 and column 6 establish the module rhythm and connect the finder regions.

Dark module

One fixed dark module sits at row 4V + 9, column 8. It is always on and is separate from the nearby format copy.

02 / Metadata

The decoder receives instructions before content

Format and version information are encoded with BCH error protection. Format information is written twice so damage near one finder does not remove the decoder instructions.

EC level, mask and format protection

The 15-bit format value contains 2 error-correction-level bits and 3 mask-pattern bits. Ten BCH protection bits are appended, then the result is XOR-masked with a fixed pattern. The same value appears in two locations.

Version information

Versions 7 through 40 store an 18-bit protected version value in two 3-by-6 areas. Smaller versions communicate their size directly through matrix dimensions.

03 / Encoded stream

Headers and payload are bit fields, not always bytes

Automatic segmentation can switch modes when the reduced payload size is worth another mode and count header. Every segment starts with its own mode and character-count fields.

Mode and character count

The 4-bit mode indicator selects Numeric, Alphanumeric, Byte or Kanji. Count-field width depends on both mode and version range; Byte mode counts encoded bytes.

Payload units

Each example below is a complete Version 1 segment header and payload. The count field changes width by mode; Byte counts encoded bytes rather than visible characters.

Numeric1233 digits
Mode0001 Count Payload

AlphanumericAB2 characters
Mode0010 Count Payload

Byteé2 UTF-8 bytes
Mode0100 Count Payload

Kanji漢1 character
Mode1000 Count Payload

Automatic mixed mode1234567890HELLO-world
Repeated green Mode and orange Count fields mark each segment before its blue payload.

Each colored block is a separate segment with another 4-bit mode indicator and count field. The optimizer keeps a switch only when its smaller payload offsets that header cost. Automatic detection does not select Kanji; Kanji must be requested explicitly.

Terminator and padding

After the last segment, up to four zero terminator bits are added. More zero bits reach a byte boundary; alternating 0xEC and 0x11 pad codewords fill the data capacity.

Remainder bits

Some versions leave 3, 4 or 7 traversable modules after all complete codewords. These zero remainder bits complete the matrix geometry; they are not data or error correction.

04 / Recovery and placement

Codewords are protected, interleaved, placed and masked

Error correction does not simply occupy a rectangular corner. Data and recovery codewords follow the same two-column zigzag placement path after block interleaving.

Data and Reed-Solomon EC words

The selected version and recovery level define one or more Reed-Solomon blocks over GF(256). Data and EC codewords are interleaved across blocks before placement, spreading localized damage across recoverable symbols.

L about 7%M about 15%Q about 25%H about 30%

Required mask

One of eight formulas flips selected non-functional modules. The encoder scores all candidates for long runs, 2-by-2 blocks, finder-like patterns and dark/light balance, then records the winner in format information.

Eight mask candidates

The formula changes; the landmarks do not

For every non-functional module at row r and column c, a true formula flips the stored bit. Blue shows where each formula is active. Finder, alignment and timing patterns remain as dark reference landmarks because masking never changes them.

Mask 0(r + c) mod 2 = 0
Mask 1r mod 2 = 0
Mask 2c mod 3 = 0
Mask 3(r + c) mod 3 = 0
Mask 4(floor(r / 2) + floor(c / 3)) mod 2 = 0
Mask 5(r x c) mod 2 + (r x c) mod 3 = 0
Mask 6(((r x c) mod 2) + ((r x c) mod 3)) mod 2 = 0
Mask 7(((r + c) mod 2) + ((r x c) mod 3)) mod 2 = 0
How Auto chooses 1. Penalize long same-color runs. 2. Penalize solid 2-by-2 blocks. 3. Penalize finder-like 1:1:3:1:1 sequences. 4. Penalize an uneven dark/light balance.

05 / Decoder order

What a scanner conceptually does

  1. 1
    Locate and sample

    Use finder, separator, timing and alignment patterns to estimate the module grid.

  2. 2
    Read metadata

    Decode format information, select the EC level and mask, and read version information when present.

  3. 3
    Unmask and traverse

    Reverse the selected mask on non-functional modules and collect codeword bits along the two-column zigzag path.

  4. 4
    Deinterleave and correct

    Reconstruct Reed-Solomon blocks, detect errors and recover codewords where redundancy permits.

  5. 5
    Parse segments

    Read each mode and count header, then decode its payload units until the terminator or data capacity is reached.

Primary references

Standards and implementation references

This guide is explanatory, not a substitute for the normative standard. Exact block tables, count widths, mask penalties and encoding rules are implemented by the generator and tested against reference matrices.

ISO/IEC 18004:2024Normative QR Code symbology specification DENSO WAVE standards historyQR Code development and standardization DENSO module configurationFunctional-pattern overview DENSO error correctionRecovery levels and symbol capacity tradeoffs Reed and Solomon, 1960Original error-correcting-code paper