FA-72175 / Error-correcting codes / Member archive

QR format BCH division skips the lowest step · case 05

Remainders are left unreduced for some data values.

Member previewVariant 5 · 3 implementations · 8 checks per implementation

Case contract

QR code format information, a BCH(15,5) code. "encode" takes [level, mask] with level bits L=01, M=00, Q=11, H=10 and mask 0..7 (else None): data = level<<3 | mask, append the 10-bit remainder of data*x^10 modulo 0x537, then XOR 0x5412. "decode" takes a 15-bit integer and returns [level, mask, distance] for the unique format word within Hamming distance 3, else None.

Why this case matters

QR readers must recover the error-correction level and mask pattern before decoding any data module.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
regression ["decode", 2309]	`["H", 7, 2]`	`["H", 6, 3]`	Failed

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