{"abstract":"Received words are \"corrected\" by high-weight patterns instead of the most likely error.","category":"Error-correcting codes","checks":8,"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).","contract_signature":"H, r","evaluation_group":"w2-error_correcting_codes-syndrome-table-decode","failed_approach":"Enumerating equal-weight patterns in reverse order breaks the stated lexicographic tie rule.","family":"w2-error_correcting_codes-syndrome-table-decode-leader-selection","id":"FA-72136","implementations":{"attempt":{"sha256":"5930df600e06d84917ebb4e5032eed40e637a6f68b986aae1e2b7b43345becef","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport itertools\nN = 1\nobservations = []\ndef solve(H, r):\n    n = len(H[0])\n    def syn(v):\n        return tuple(sum(h[k] & v[k] for k in range(n)) % 2 for h in H)\n    table = {}\n    for w in range(n + 1):\n        for pos in reversed(list(itertools.combinations(range(n), w))):\n            e = [1 if k in pos else 0 for k in range(n)]\n            table.setdefault(syn(e), e)\n    e = table.get(syn(r))\n    if e is None:\n        return None\n    return [[a ^ b for a, b in zip(r, e)], sum(e)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...', [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1]], [0, 0, 0, 0, 0, 1, 0]], [[0, 0, 0, 0, 0, 0, 0], 1]], ['regression [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...', [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1]], [0, 1, 1, 1, 0, 0, 0]], [[0, 1, 1, 1, 0, 0, 1], 1]], ['partial-repair [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 0, 0, 1, 0]]', [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 0, 0, 1, 0]], [[0, 1, 0, 1, 0], 1]], ['partial-repair [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [1, 1, 1, 0, 1]]', [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [1, 1, 1, 0, 1]], [[0, 1, 1, 0, 1], 1]], ['control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...', [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1]], [0, 0, 1, 1, 0, 1, 1]], [[0, 0, 1, 1, 0, 1, 0], 1]], ['control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...', [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1]], [0, 0, 0, 1, 1, 0, 0]], [[0, 1, 0, 1, 1, 0, 0], 1]], ['control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...', [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1]], [0, 1, 1, 1, 0, 1, 1]], [[0, 1, 1, 1, 0, 0, 1], 1]], ['control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...', [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1]], [1, 1, 1, 1, 0, 1, 1]], [[1, 1, 1, 1, 1, 1, 1], 1]]], [['regression [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...', [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1]], [0, 0, 0, 1, 1, 0, 0]], [[0, 1, 0, 1, 1, 0, 0], 1]], ['regression [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...', [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1]], [0, 1, 1, 1, 0, 1, 1]], [[0, 1, 1, 1, 0, 0, 1], 1]], ['partial-repair [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [1, 1, 1, 0, 1]]', [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [1, 1, 1, 0, 1]], [[0, 1, 1, 0, 1], 1]], ['partial-repair [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 0, 0, 1, 0]]', [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 0, 0, 1, 0]], [[0, 1, 0, 1, 0], 1]], ['control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...', [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1]], [1, 1, 1, 1, 0, 1, 1]], [[1, 1, 1, 1, 1, 1, 1], 1]], ['control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...', [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1]], [0, 0, 1, 0, 1, 0, 1]], [[0, 0, 1, 0, 1, 0, 1], 0]], ['control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...', [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1]], [1, 1, 0, 1, 1, 0, 1]], [[1, 1, 0, 0, 1, 0, 1], 1]], ['control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...', [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1]], [1, 0, 0, 0, 1, 0, 1]], [[1, 1, 0, 0, 1, 0, 1], 1]]], [['regression [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...', [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1]], [0, 0, 1, 0, 1, 0, 1]], [[0, 0, 1, 0, 1, 0, 1], 0]], ['regression [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...', [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1]], [1, 1, 0, 1, 1, 0, 1]], [[1, 1, 0, 0, 1, 0, 1], 1]], ['partial-repair [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 0, 0, 1, 0]]', [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 0, 0, 1, 0]], [[0, 1, 0, 1, 0], 1]], ['partial-repair [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [1, 1, 1, 0, 1]]', [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [1, 1, 1, 0, 1]], [[0, 1, 1, 0, 1], 1]], ['control [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, ...', [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, 1, 0, 0, 1, 0]], [[1, 1, 0, 0, 1, 1], 1]], ['control [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, ...', [[[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, 0, 0, 0, 0, 0], 1]], ['control [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, ...', [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, 0, 1, 1, 0, 1]], [[1, 0, 0, 1, 0, 1], 1]], ['control [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, ...', [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, 0, 1, 1, 0, 0]], [[1, 0, 1, 1, 1, 0], 1]]], [['regression [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, ...', [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, 0, 1, 1, 1, 0]], [[1, 0, 1, 1, 1, 0], 0]], ['regression [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, ...', [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, 1, 0, 0, 1, 0]], [[1, 1, 0, 0, 1, 1], 1]], ['partial-repair [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [1, 1, 1, 0, 1]]', [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [1, 1, 1, 0, 1]], [[0, 1, 1, 0, 1], 1]], ['partial-repair [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 0, 0, 1, 0]]', [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 0, 0, 1, 0]], [[0, 1, 0, 1, 0], 1]], ['control [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [0, ...', [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [0, 1, 0, 0, 0, 0]], [[0, 0, 0, 0, 0, 0], 1]], ['control [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [0, ...', [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [0, 0, 1, 0, 1, 1]], [[0, 0, 1, 0, 1, 1], 0]], ['control [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 1, 1, 0, 0]]', [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 1, 1, 0, 0]], [[0, 1, 1, 0, 1], 1]], ['control [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 1, 1, 0, 1]]', [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 1, 1, 0, 1]], [[0, 1, 1, 0, 1], 0]]], [['regression [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, ...', [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, 0, 1, 1, 0, 1]], [[1, 0, 0, 1, 0, 1], 1]], ['regression [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, ...', [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, 0, 1, 1, 0, 0]], [[1, 0, 1, 1, 1, 0], 1]], ['partial-repair [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 0, 0, 1, 0]]', [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 0, 0, 1, 0]], [[0, 1, 0, 1, 0], 1]], ['partial-repair [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [1, 1, 1, 0, 1]]', [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [1, 1, 1, 0, 1]], [[0, 1, 1, 0, 1], 1]], ['control [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 1, 0, 1, 1]]', [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 1, 0, 1, 1]], [[0, 1, 0, 1, 0], 1]], ['control [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 0, 1, 1, 0]]', [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 0, 1, 1, 0]], [[0, 0, 1, 1, 1], 1]], ['control [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [1, 0, 1, 0, 1]]', [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [1, 0, 1, 0, 1]], [[1, 0, 1, 0, 0], 1]], ['control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...', [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1]], [0, 0, 0, 0, 0, 1, 0]], [[0, 0, 0, 0, 0, 0, 0], 1]]]]\nfor label, args, expected in fixtures[N - 1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"2822b91adbac900f8b6e158edea6f97184b7882469c4124bc930438c297e816e","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport itertools\nN = 1\nobservations = []\ndef solve(H, r):\n    n = len(H[0])\n    def syn(v):\n        return tuple(sum(h[k] & v[k] for k in range(n)) % 2 for h in H)\n    table = {}\n    for w in range(n + 1):\n        for pos in itertools.combinations(range(n), w):\n            e = [1 if k in pos else 0 for k in range(n)]\n            table[syn(e)] = e\n    e = table.get(syn(r))\n    if e is None:\n        return None\n    return [[a ^ b for a, b in zip(r, e)], sum(e)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...', [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1]], [0, 0, 0, 0, 0, 1, 0]], [[0, 0, 0, 0, 0, 0, 0], 1]], ['regression [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...', [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1]], [0, 1, 1, 1, 0, 0, 0]], [[0, 1, 1, 1, 0, 0, 1], 1]], ['partial-repair [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 0, 0, 1, 0]]', [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 0, 0, 1, 0]], [[0, 1, 0, 1, 0], 1]], ['partial-repair [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [1, 1, 1, 0, 1]]', [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [1, 1, 1, 0, 1]], [[0, 1, 1, 0, 1], 1]], ['control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...', [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1]], [0, 0, 1, 1, 0, 1, 1]], [[0, 0, 1, 1, 0, 1, 0], 1]], ['control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...', [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1]], [0, 0, 0, 1, 1, 0, 0]], [[0, 1, 0, 1, 1, 0, 0], 1]], ['control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...', [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1]], [0, 1, 1, 1, 0, 1, 1]], [[0, 1, 1, 1, 0, 0, 1], 1]], ['control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...', [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1]], [1, 1, 1, 1, 0, 1, 1]], [[1, 1, 1, 1, 1, 1, 1], 1]]], [['regression [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...', [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1]], [0, 0, 0, 1, 1, 0, 0]], [[0, 1, 0, 1, 1, 0, 0], 1]], ['regression [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...', [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1]], [0, 1, 1, 1, 0, 1, 1]], [[0, 1, 1, 1, 0, 0, 1], 1]], ['partial-repair [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [1, 1, 1, 0, 1]]', [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [1, 1, 1, 0, 1]], [[0, 1, 1, 0, 1], 1]], ['partial-repair [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 0, 0, 1, 0]]', [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 0, 0, 1, 0]], [[0, 1, 0, 1, 0], 1]], ['control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...', [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1]], [1, 1, 1, 1, 0, 1, 1]], [[1, 1, 1, 1, 1, 1, 1], 1]], ['control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...', [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1]], [0, 0, 1, 0, 1, 0, 1]], [[0, 0, 1, 0, 1, 0, 1], 0]], ['control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...', [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1]], [1, 1, 0, 1, 1, 0, 1]], [[1, 1, 0, 0, 1, 0, 1], 1]], ['control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...', [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1]], [1, 0, 0, 0, 1, 0, 1]], [[1, 1, 0, 0, 1, 0, 1], 1]]], [['regression [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...', [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1]], [0, 0, 1, 0, 1, 0, 1]], [[0, 0, 1, 0, 1, 0, 1], 0]], ['regression [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...', [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1]], [1, 1, 0, 1, 1, 0, 1]], [[1, 1, 0, 0, 1, 0, 1], 1]], ['partial-repair [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 0, 0, 1, 0]]', [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 0, 0, 1, 0]], [[0, 1, 0, 1, 0], 1]], ['partial-repair [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [1, 1, 1, 0, 1]]', [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [1, 1, 1, 0, 1]], [[0, 1, 1, 0, 1], 1]], ['control [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, ...', [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, 1, 0, 0, 1, 0]], [[1, 1, 0, 0, 1, 1], 1]], ['control [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, ...', [[[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, 0, 0, 0, 0, 0], 1]], ['control [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, ...', [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, 0, 1, 1, 0, 1]], [[1, 0, 0, 1, 0, 1], 1]], ['control [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, ...', [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, 0, 1, 1, 0, 0]], [[1, 0, 1, 1, 1, 0], 1]]], [['regression [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, ...', [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, 0, 1, 1, 1, 0]], [[1, 0, 1, 1, 1, 0], 0]], ['regression [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, ...', [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, 1, 0, 0, 1, 0]], [[1, 1, 0, 0, 1, 1], 1]], ['partial-repair [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [1, 1, 1, 0, 1]]', [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [1, 1, 1, 0, 1]], [[0, 1, 1, 0, 1], 1]], ['partial-repair [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 0, 0, 1, 0]]', [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 0, 0, 1, 0]], [[0, 1, 0, 1, 0], 1]], ['control [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [0, ...', [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [0, 1, 0, 0, 0, 0]], [[0, 0, 0, 0, 0, 0], 1]], ['control [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [0, ...', [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [0, 0, 1, 0, 1, 1]], [[0, 0, 1, 0, 1, 1], 0]], ['control [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 1, 1, 0, 0]]', [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 1, 1, 0, 0]], [[0, 1, 1, 0, 1], 1]], ['control [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 1, 1, 0, 1]]', [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 1, 1, 0, 1]], [[0, 1, 1, 0, 1], 0]]], [['regression [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, ...', [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, 0, 1, 1, 0, 1]], [[1, 0, 0, 1, 0, 1], 1]], ['regression [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, ...', [[[1, 1, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 0, 1]], [1, 0, 1, 1, 0, 0]], [[1, 0, 1, 1, 1, 0], 1]], ['partial-repair [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 0, 0, 1, 0]]', [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 0, 0, 1, 0]], [[0, 1, 0, 1, 0], 1]], ['partial-repair [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [1, 1, 1, 0, 1]]', [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [1, 1, 1, 0, 1]], [[0, 1, 1, 0, 1], 1]], ['control [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 1, 0, 1, 1]]', [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 1, 0, 1, 1]], [[0, 1, 0, 1, 0], 1]], ['control [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 0, 1, 1, 0]]', [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 0, 1, 1, 0]], [[0, 0, 1, 1, 1], 1]], ['control [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [1, 0, 1, 0, 1]]', [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [1, 0, 1, 0, 1]], [[1, 0, 1, 0, 0], 1]], ['control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...', [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, 1]], [0, 0, 0, 0, 0, 1, 0]], [[0, 0, 0, 0, 0, 0, 0], 1]]]]\nfor label, args, expected in fixtures[N - 1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"A deterministic, bounded teaching model of the named code under the stated contract; not a production codec. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"w2-error_correcting_codes-syndrome-table-decode-leader-selection","generated_at":"2026-09-29T14:48:35.885699+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Short block codes in control channels are decoded with precomputed coset-leader tables.","root_cause":"The table assignment overwrites earlier entries, so the last (heaviest) pattern becomes the leader.","sha256":"748e0156b6e1a1234262569c85ca6985706d495245434479c4316569142800a4","title":"Syndrome table keeps the heaviest coset member · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":41.205,"exit_code":1,"observations":[{"actual":[[0,0,0,0,0,0,0],1],"check":"regression [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...","expected":[[0,0,0,0,0,0,0],1],"passed":true},{"actual":[[0,1,1,1,0,0,1],1],"check":"regression [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...","expected":[[0,1,1,1,0,0,1],1],"passed":true},{"actual":[[0,0,0,0,0],1],"check":"partial-repair [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 0, 0, 1, 0]]","expected":[[0,1,0,1,0],1],"passed":false},{"actual":[[1,1,0,0,1],1],"check":"partial-repair [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [1, 1, 1, 0, 1]]","expected":[[0,1,1,0,1],1],"passed":false},{"actual":[[0,0,1,1,0,1,0],1],"check":"control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...","expected":[[0,0,1,1,0,1,0],1],"passed":true},{"actual":[[0,1,0,1,1,0,0],1],"check":"control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...","expected":[[0,1,0,1,1,0,0],1],"passed":true},{"actual":[[0,1,1,1,0,0,1],1],"check":"control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...","expected":[[0,1,1,1,0,0,1],1],"passed":true},{"actual":[[1,1,1,1,1,1,1],1],"check":"control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...","expected":[[1,1,1,1,1,1,1],1],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...\", \"actual\": [[0, 0, 0, 0, 0, 0, 0], 1], \"expected\": [[0, 0, 0, 0, 0, 0, 0], 1], \"passed\": true}, {\"check\": \"regression [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...\", \"actual\": [[0, 1, 1, 1, 0, 0, 1], 1], \"expected\": [[0, 1, 1, 1, 0, 0, 1], 1], \"passed\": true}, {\"check\": \"partial-repair [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 0, 0, 1, 0]]\", \"actual\": [[0, 0, 0, 0, 0], 1], \"expected\": [[0, 1, 0, 1, 0], 1], \"passed\": false}, {\"check\": \"partial-repair [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [1, 1, 1, 0, 1]]\", \"actual\": [[1, 1, 0, 0, 1], 1], \"expected\": [[0, 1, 1, 0, 1], 1], \"passed\": false}, {\"check\": \"control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...\", \"actual\": [[0, 0, 1, 1, 0, 1, 0], 1], \"expected\": [[0, 0, 1, 1, 0, 1, 0], 1], \"passed\": true}, {\"check\": \"control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...\", \"actual\": [[0, 1, 0, 1, 1, 0, 0], 1], \"expected\": [[0, 1, 0, 1, 1, 0, 0], 1], \"passed\": true}, {\"check\": \"control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...\", \"actual\": [[0, 1, 1, 1, 0, 0, 1], 1], \"expected\": [[0, 1, 1, 1, 0, 0, 1], 1], \"passed\": true}, {\"check\": \"control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...\", \"actual\": [[1, 1, 1, 1, 1, 1, 1], 1], \"expected\": [[1, 1, 1, 1, 1, 1, 1], 1], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":41.581,"exit_code":1,"observations":[{"actual":[[1,1,1,1,1,1,1],6],"check":"regression [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...","expected":[[0,0,0,0,0,0,0],1],"passed":false},{"actual":[[1,0,0,0,1,1,0],6],"check":"regression [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...","expected":[[0,1,1,1,0,0,1],1],"passed":false},{"actual":[[0,1,1,0,1],4],"check":"partial-repair [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 0, 0, 1, 0]]","expected":[[0,1,0,1,0],1],"passed":false},{"actual":[[0,1,0,1,0],4],"check":"partial-repair [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [1, 1, 1, 0, 1]]","expected":[[0,1,1,0,1],1],"passed":false},{"actual":[[1,1,0,0,1,0,1],6],"check":"control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...","expected":[[0,0,1,1,0,1,0],1],"passed":false},{"actual":[[1,0,1,0,0,1,1],6],"check":"control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...","expected":[[0,1,0,1,1,0,0],1],"passed":false},{"actual":[[1,0,0,0,1,1,0],6],"check":"control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...","expected":[[0,1,1,1,0,0,1],1],"passed":false},{"actual":[[0,0,0,0,0,0,0],6],"check":"control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...","expected":[[1,1,1,1,1,1,1],1],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...\", \"actual\": [[1, 1, 1, 1, 1, 1, 1], 6], \"expected\": [[0, 0, 0, 0, 0, 0, 0], 1], \"passed\": false}, {\"check\": \"regression [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...\", \"actual\": [[1, 0, 0, 0, 1, 1, 0], 6], \"expected\": [[0, 1, 1, 1, 0, 0, 1], 1], \"passed\": false}, {\"check\": \"partial-repair [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [0, 0, 0, 1, 0]]\", \"actual\": [[0, 1, 1, 0, 1], 4], \"expected\": [[0, 1, 0, 1, 0], 1], \"passed\": false}, {\"check\": \"partial-repair [[[1, 1, 1, 1, 0], [1, 0, 1, 0, 1]], [1, 1, 1, 0, 1]]\", \"actual\": [[0, 1, 0, 1, 0], 4], \"expected\": [[0, 1, 1, 0, 1], 1], \"passed\": false}, {\"check\": \"control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...\", \"actual\": [[1, 1, 0, 0, 1, 0, 1], 6], \"expected\": [[0, 0, 1, 1, 0, 1, 0], 1], \"passed\": false}, {\"check\": \"control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...\", \"actual\": [[1, 0, 1, 0, 0, 1, 1], 6], \"expected\": [[0, 1, 0, 1, 1, 0, 0], 1], \"passed\": false}, {\"check\": \"control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...\", \"actual\": [[1, 0, 0, 0, 1, 1, 0], 6], \"expected\": [[0, 1, 1, 1, 0, 0, 1], 1], \"passed\": false}, {\"check\": \"control [[[1, 0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0, ...\", \"actual\": [[0, 0, 0, 0, 0, 0, 0], 6], \"expected\": [[1, 1, 1, 1, 1, 1, 1], 1], \"passed\": false}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}