FA-72144 / Error-correcting codes / Member archive

Syndrome table uses integer check sums · case 04

Syndromes of different cosets collide or miss the table.

Member previewVariant 4 · 3 implementations · 8 checks per implementation

Case contract

Syndrome decoding of a binary linear code from its parity-check matrix H (rows). The coset-leader table is built by enumerating error patterns by increasing weight and, within a weight, in lexicographic order of error positions; the first pattern seen for a syndrome is its leader. Decode r by XORing the leader of its syndrome. Return [codeword, leader weight] (None if the syndrome has no leader).

Why this case matters

Short block codes in control channels are decoded with precomputed coset-leader tables.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
regression [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, ...	`[[0, 0, 0, 0, 0, 0], 3]`	`[[1, 1, 0, 0, 1, 1], 1]`	Failed

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