FA-72148 / Error-correcting codes / Member archive

Syndrome table ORs the error pattern into the word · case 03

Errors on bits that were received as 1 are never removed.

Member previewVariant 3 · 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]], [0, ...	`[[0, 1, 0, 0, 0, 0], 1]`	`[[0, 0, 0, 0, 0, 0], 1]`	Failed

MEMBER ARCHIVE

The complete case is available to members.

This record includes three runnable implementations, regression fixtures, execution results, and source hashes.

Member access is invitation-based. Sign in with your invited account to inspect the sources.