FA-72327 / Error-correcting codes / Member archive

BCH cosets list a coset twice · case 02

The coset list repeats a coset reached from a later representative.

Member previewVariant 2 · 3 implementations · 8 checks per implementation

Case contract

Design a binary narrow-sense BCH code of length n = 2^m - 1 correcting t errors: its generator has as roots the union of the 2-cyclotomic cosets mod n of 1..2t. Return [distinct cosets in order of first representative, each sorted, number of parity bits n - k = size of the union]. Invalid n or t < 1 returns None.

Why this case matters

BCH codes in flash memory and satellite links are specified by their cyclotomic cosets.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
regression [15, 2]	`[[[1, 2, 4, 8], [1, 2, 4, 8], [3, 6, 9, 12], [1, 2, 4, 8]], 8]`	`[[[1, 2, 4, 8], [3, 6, 9, 12]], 8]`	Failed

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