{"abstract":"Minimum distance is overstated when a combination of rows is lighter than every row.","category":"Error-correcting codes","checks":8,"contract":"Weight distribution of the binary linear code spanned by the rows of generator matrix G (rows may be dependent). Enumerate all 2^k messages including the zero message, form codewords as XOR combinations of rows, and histogram their Hamming weights (index 0..n). dmin is the smallest nonzero weight present (0 if the code is only the zero word). Return [histogram, dmin].","contract_signature":"G","evaluation_group":"w2-error_correcting_codes-weight-distribution","failed_approach":"Including weight 0 in the search always reports distance 0.","family":"w2-error_correcting_codes-weight-distribution-minimum-weight","id":"FA-72296","implementations":{"attempt":{"sha256":"6373818cfdafff9294471df28800dfb34617b6247be96faeef441b4df1cd0eea","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(G):\n    k, n = len(G), len(G[0])\n    hist = [0] * (n + 1)\n    for msg in range(2 ** k):\n        c = [0] * n\n        for i in range(k):\n            if msg >> i & 1:\n                c = [a ^ b for a, b in zip(c, G[i])]\n        hist[sum(c)] += 1\n    dmin = min(w for w in range(0, n + 1) if hist[w]) if any(hist[1:]) else 0\n    return [hist, dmin]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]]', [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]], [[2, 2, 4, 4, 2, 2], 1]], ['regression [[[0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, ...', [[[0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 0, 0]]], [[1, 1, 6, 6, 1, 1, 0, 0], 1]], ['partial-repair [[[1, 0, 0, 0, 1, 1, 0], [0, 1, 0, 0, 1, 0, 1], [0, 0, 1, 0, 0, 1, ...', [[[1, 0, 0, 0, 1, 1, 0], [0, 1, 0, 0, 1, 0, 1], [0, 0, 1, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1, 1]]], [[1, 0, 0, 7, 7, 0, 0, 1], 3]], ['partial-repair [[[1, 1, 1]]]', [[[1, 1, 1]]], [[1, 0, 0, 1], 3]], ['control [[[0, 0, 0]]]', [[[0, 0, 0]]], [[2, 0, 0, 0], 0]], ['control [[[1, 1, 0, 0], [0, 1, 1, 0], [0, 0, 1, 1]]]', [[[1, 1, 0, 0], [0, 1, 1, 0], [0, 0, 1, 1]]], [[1, 0, 6, 0, 1], 2]], ['control [[[1, 0, 1, 1, 0], [0, 1, 1, 1, 1]]]', [[[1, 0, 1, 1, 0], [0, 1, 1, 1, 1]]], [[1, 0, 0, 2, 1, 0], 3]], ['control [[[1, 1, 0], [1, 1, 0]]]', [[[1, 1, 0], [1, 1, 0]]], [[2, 0, 2, 0], 2]]], [['regression [[[0, 0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 0, 1, 1], [1, 1, 1, 0, 1, 1, ...', [[[0, 0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 0, 1, 1], [1, 1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0, 1]]], [[1, 1, 1, 4, 5, 3, 1, 0], 1]], ['regression [[[0, 1, 1, 1, 1, 0, 0], [0, 1, 1, 0, 1, 1, 1], [1, 0, 0, 0, 1, 1, ...', [[[0, 1, 1, 1, 1, 0, 0], [0, 1, 1, 0, 1, 1, 1], [1, 0, 0, 0, 1, 1, 1]]], [[1, 0, 0, 3, 2, 1, 1, 0], 3]], ['partial-repair [[[1, 0, 1, 1, 0], [0, 1, 1, 1, 1]]]', [[[1, 0, 1, 1, 0], [0, 1, 1, 1, 1]]], [[1, 0, 0, 2, 1, 0], 3]], ['partial-repair [[[1, 1, 0], [1, 1, 0]]]', [[[1, 1, 0], [1, 1, 0]]], [[2, 0, 2, 0], 2]], ['control [[[0, 0, 0]]]', [[[0, 0, 0]]], [[2, 0, 0, 0], 0]], ['control [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]]', [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]], [[2, 2, 4, 4, 2, 2], 1]], ['control [[[0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, ...', [[[0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 0, 0]]], [[1, 1, 6, 6, 1, 1, 0, 0], 1]], ['control [[[1, 1, 1, 1, 1, 1, 1], [1, 0, 1, 1, 1, 0, 0], [0, 1, 1, 0, 0, 0, ...', [[[1, 1, 1, 1, 1, 1, 1], [1, 0, 1, 1, 1, 0, 0], [0, 1, 1, 0, 0, 0, 0], [1, 1, 1, 0, 0, 1, 0]]], [[1, 0, 2, 5, 5, 2, 0, 1], 2]]], [['regression [[[0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, ...', [[[0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 0, 0]]], [[1, 1, 6, 6, 1, 1, 0, 0], 1]], ['regression [[[1, 0, 0, 1, 1, 0], [1, 1, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0]]]', [[[1, 0, 0, 1, 1, 0], [1, 1, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0]]], [[1, 1, 1, 3, 2, 0, 0], 1]], ['partial-repair [[[1, 1, 1, 1, 1, 1, 1], [1, 0, 1, 1, 1, 0, 0], [0, 1, 1, 0, 0, 0, ...', [[[1, 1, 1, 1, 1, 1, 1], [1, 0, 1, 1, 1, 0, 0], [0, 1, 1, 0, 0, 0, 0], [1, 1, 1, 0, 0, 1, 0]]], [[1, 0, 2, 5, 5, 2, 0, 1], 2]], ['control [[[0, 0, 0]]]', [[[0, 0, 0]]], [[2, 0, 0, 0], 0]], ['control [[[1, 1, 1, 0, 0, 0, 1]]]', [[[1, 1, 1, 0, 0, 0, 1]]], [[1, 0, 0, 0, 1, 0, 0, 0], 4]], ['control [[[1, 0, 1, 1], [0, 0, 0, 1]]]', [[[1, 0, 1, 1], [0, 0, 0, 1]]], [[1, 1, 1, 1, 0], 1]], ['control [[[1, 0]]]', [[[1, 0]]], [[1, 1, 0], 1]], ['control [[[0, 0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 0, 1, 1], [1, 1, 1, 0, 1, 1, ...', [[[0, 0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 0, 1, 1], [1, 1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0, 1]]], [[1, 1, 1, 4, 5, 3, 1, 0], 1]]], [['regression [[[0, 1, 1, 1, 1, 0, 0], [0, 1, 1, 0, 1, 1, 1], [1, 0, 0, 0, 1, 1, ...', [[[0, 1, 1, 1, 1, 0, 0], [0, 1, 1, 0, 1, 1, 1], [1, 0, 0, 0, 1, 1, 1]]], [[1, 0, 0, 3, 2, 1, 1, 0], 3]], ['regression [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]]', [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]], [[2, 2, 4, 4, 2, 2], 1]], ['partial-repair [[[1, 0, 0, 1, 1, 0], [1, 1, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0]]]', [[[1, 0, 0, 1, 1, 0], [1, 1, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0]]], [[1, 1, 1, 3, 2, 0, 0], 1]], ['partial-repair [[[1, 1, 1, 0, 0, 0, 1]]]', [[[1, 1, 1, 0, 0, 0, 1]]], [[1, 0, 0, 0, 1, 0, 0, 0], 4]], ['control [[[0, 0, 0]]]', [[[0, 0, 0]]], [[2, 0, 0, 0], 0]], ['control [[[0, 1, 0, 0, 1, 0, 0], [1, 1, 1, 0, 1, 1, 0], [1, 1, 0, 1, 1, 1, ...', [[[0, 1, 0, 0, 1, 0, 0], [1, 1, 1, 0, 1, 1, 0], [1, 1, 0, 1, 1, 1, 0]]], [[1, 0, 2, 2, 1, 2, 0, 0], 2]], ['control [[[0, 0, 1], [1, 1, 0]]]', [[[0, 0, 1], [1, 1, 0]]], [[1, 1, 1, 1], 1]], ['control [[[0, 0, 1, 0]]]', [[[0, 0, 1, 0]]], [[1, 1, 0, 0, 0], 1]]], [['regression [[[1, 0, 0, 1, 1, 0], [1, 1, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0]]]', [[[1, 0, 0, 1, 1, 0], [1, 1, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0]]], [[1, 1, 1, 3, 2, 0, 0], 1]], ['regression [[[0, 0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 0, 1, 1], [1, 1, 1, 0, 1, 1, ...', [[[0, 0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 0, 1, 1], [1, 1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0, 1]]], [[1, 1, 1, 4, 5, 3, 1, 0], 1]], ['partial-repair [[[1, 0]]]', [[[1, 0]]], [[1, 1, 0], 1]], ['control [[[0, 0, 0]]]', [[[0, 0, 0]]], [[2, 0, 0, 0], 0]], ['control [[[1, 0, 0, 0, 1, 1, 0], [0, 1, 0, 0, 1, 0, 1], [0, 0, 1, 0, 0, 1, ...', [[[1, 0, 0, 0, 1, 1, 0], [0, 1, 0, 0, 1, 0, 1], [0, 0, 1, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1, 1]]], [[1, 0, 0, 7, 7, 0, 0, 1], 3]], ['control [[[1, 1, 1]]]', [[[1, 1, 1]]], [[1, 0, 0, 1], 3]], ['control [[[1, 1, 0, 0], [0, 1, 1, 0], [0, 0, 1, 1]]]', [[[1, 1, 0, 0], [0, 1, 1, 0], [0, 0, 1, 1]]], [[1, 0, 6, 0, 1], 2]], ['control [[[1, 0, 1, 1, 0], [0, 1, 1, 1, 1]]]', [[[1, 0, 1, 1, 0], [0, 1, 1, 1, 1]]], [[1, 0, 0, 2, 1, 0], 3]]]]\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":"7418cc3e62934522aca00556eb2408f1a100f2347795c03c9c8a1d93fbf38509","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(G):\n    k, n = len(G), len(G[0])\n    hist = [0] * (n + 1)\n    for msg in range(2 ** k):\n        c = [0] * n\n        for i in range(k):\n            if msg >> i & 1:\n                c = [a ^ b for a, b in zip(c, G[i])]\n        hist[sum(c)] += 1\n    dmin = min(sum(row) for row in G)\n    return [hist, dmin]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]]', [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]], [[2, 2, 4, 4, 2, 2], 1]], ['regression [[[0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, ...', [[[0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 0, 0]]], [[1, 1, 6, 6, 1, 1, 0, 0], 1]], ['partial-repair [[[1, 0, 0, 0, 1, 1, 0], [0, 1, 0, 0, 1, 0, 1], [0, 0, 1, 0, 0, 1, ...', [[[1, 0, 0, 0, 1, 1, 0], [0, 1, 0, 0, 1, 0, 1], [0, 0, 1, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1, 1]]], [[1, 0, 0, 7, 7, 0, 0, 1], 3]], ['partial-repair [[[1, 1, 1]]]', [[[1, 1, 1]]], [[1, 0, 0, 1], 3]], ['control [[[0, 0, 0]]]', [[[0, 0, 0]]], [[2, 0, 0, 0], 0]], ['control [[[1, 1, 0, 0], [0, 1, 1, 0], [0, 0, 1, 1]]]', [[[1, 1, 0, 0], [0, 1, 1, 0], [0, 0, 1, 1]]], [[1, 0, 6, 0, 1], 2]], ['control [[[1, 0, 1, 1, 0], [0, 1, 1, 1, 1]]]', [[[1, 0, 1, 1, 0], [0, 1, 1, 1, 1]]], [[1, 0, 0, 2, 1, 0], 3]], ['control [[[1, 1, 0], [1, 1, 0]]]', [[[1, 1, 0], [1, 1, 0]]], [[2, 0, 2, 0], 2]]], [['regression [[[0, 0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 0, 1, 1], [1, 1, 1, 0, 1, 1, ...', [[[0, 0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 0, 1, 1], [1, 1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0, 1]]], [[1, 1, 1, 4, 5, 3, 1, 0], 1]], ['regression [[[0, 1, 1, 1, 1, 0, 0], [0, 1, 1, 0, 1, 1, 1], [1, 0, 0, 0, 1, 1, ...', [[[0, 1, 1, 1, 1, 0, 0], [0, 1, 1, 0, 1, 1, 1], [1, 0, 0, 0, 1, 1, 1]]], [[1, 0, 0, 3, 2, 1, 1, 0], 3]], ['partial-repair [[[1, 0, 1, 1, 0], [0, 1, 1, 1, 1]]]', [[[1, 0, 1, 1, 0], [0, 1, 1, 1, 1]]], [[1, 0, 0, 2, 1, 0], 3]], ['partial-repair [[[1, 1, 0], [1, 1, 0]]]', [[[1, 1, 0], [1, 1, 0]]], [[2, 0, 2, 0], 2]], ['control [[[0, 0, 0]]]', [[[0, 0, 0]]], [[2, 0, 0, 0], 0]], ['control [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]]', [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]], [[2, 2, 4, 4, 2, 2], 1]], ['control [[[0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, ...', [[[0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 0, 0]]], [[1, 1, 6, 6, 1, 1, 0, 0], 1]], ['control [[[1, 1, 1, 1, 1, 1, 1], [1, 0, 1, 1, 1, 0, 0], [0, 1, 1, 0, 0, 0, ...', [[[1, 1, 1, 1, 1, 1, 1], [1, 0, 1, 1, 1, 0, 0], [0, 1, 1, 0, 0, 0, 0], [1, 1, 1, 0, 0, 1, 0]]], [[1, 0, 2, 5, 5, 2, 0, 1], 2]]], [['regression [[[0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, ...', [[[0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 0, 0]]], [[1, 1, 6, 6, 1, 1, 0, 0], 1]], ['regression [[[1, 0, 0, 1, 1, 0], [1, 1, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0]]]', [[[1, 0, 0, 1, 1, 0], [1, 1, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0]]], [[1, 1, 1, 3, 2, 0, 0], 1]], ['partial-repair [[[1, 1, 1, 1, 1, 1, 1], [1, 0, 1, 1, 1, 0, 0], [0, 1, 1, 0, 0, 0, ...', [[[1, 1, 1, 1, 1, 1, 1], [1, 0, 1, 1, 1, 0, 0], [0, 1, 1, 0, 0, 0, 0], [1, 1, 1, 0, 0, 1, 0]]], [[1, 0, 2, 5, 5, 2, 0, 1], 2]], ['control [[[0, 0, 0]]]', [[[0, 0, 0]]], [[2, 0, 0, 0], 0]], ['control [[[1, 1, 1, 0, 0, 0, 1]]]', [[[1, 1, 1, 0, 0, 0, 1]]], [[1, 0, 0, 0, 1, 0, 0, 0], 4]], ['control [[[1, 0, 1, 1], [0, 0, 0, 1]]]', [[[1, 0, 1, 1], [0, 0, 0, 1]]], [[1, 1, 1, 1, 0], 1]], ['control [[[1, 0]]]', [[[1, 0]]], [[1, 1, 0], 1]], ['control [[[0, 0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 0, 1, 1], [1, 1, 1, 0, 1, 1, ...', [[[0, 0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 0, 1, 1], [1, 1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0, 1]]], [[1, 1, 1, 4, 5, 3, 1, 0], 1]]], [['regression [[[0, 1, 1, 1, 1, 0, 0], [0, 1, 1, 0, 1, 1, 1], [1, 0, 0, 0, 1, 1, ...', [[[0, 1, 1, 1, 1, 0, 0], [0, 1, 1, 0, 1, 1, 1], [1, 0, 0, 0, 1, 1, 1]]], [[1, 0, 0, 3, 2, 1, 1, 0], 3]], ['regression [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]]', [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]], [[2, 2, 4, 4, 2, 2], 1]], ['partial-repair [[[1, 0, 0, 1, 1, 0], [1, 1, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0]]]', [[[1, 0, 0, 1, 1, 0], [1, 1, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0]]], [[1, 1, 1, 3, 2, 0, 0], 1]], ['partial-repair [[[1, 1, 1, 0, 0, 0, 1]]]', [[[1, 1, 1, 0, 0, 0, 1]]], [[1, 0, 0, 0, 1, 0, 0, 0], 4]], ['control [[[0, 0, 0]]]', [[[0, 0, 0]]], [[2, 0, 0, 0], 0]], ['control [[[0, 1, 0, 0, 1, 0, 0], [1, 1, 1, 0, 1, 1, 0], [1, 1, 0, 1, 1, 1, ...', [[[0, 1, 0, 0, 1, 0, 0], [1, 1, 1, 0, 1, 1, 0], [1, 1, 0, 1, 1, 1, 0]]], [[1, 0, 2, 2, 1, 2, 0, 0], 2]], ['control [[[0, 0, 1], [1, 1, 0]]]', [[[0, 0, 1], [1, 1, 0]]], [[1, 1, 1, 1], 1]], ['control [[[0, 0, 1, 0]]]', [[[0, 0, 1, 0]]], [[1, 1, 0, 0, 0], 1]]], [['regression [[[1, 0, 0, 1, 1, 0], [1, 1, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0]]]', [[[1, 0, 0, 1, 1, 0], [1, 1, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0]]], [[1, 1, 1, 3, 2, 0, 0], 1]], ['regression [[[0, 0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 0, 1, 1], [1, 1, 1, 0, 1, 1, ...', [[[0, 0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 0, 1, 1], [1, 1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0, 1]]], [[1, 1, 1, 4, 5, 3, 1, 0], 1]], ['partial-repair [[[1, 0]]]', [[[1, 0]]], [[1, 1, 0], 1]], ['control [[[0, 0, 0]]]', [[[0, 0, 0]]], [[2, 0, 0, 0], 0]], ['control [[[1, 0, 0, 0, 1, 1, 0], [0, 1, 0, 0, 1, 0, 1], [0, 0, 1, 0, 0, 1, ...', [[[1, 0, 0, 0, 1, 1, 0], [0, 1, 0, 0, 1, 0, 1], [0, 0, 1, 0, 0, 1, 1], [0, 0, 0, 1, 1, 1, 1]]], [[1, 0, 0, 7, 7, 0, 0, 1], 3]], ['control [[[1, 1, 1]]]', [[[1, 1, 1]]], [[1, 0, 0, 1], 3]], ['control [[[1, 1, 0, 0], [0, 1, 1, 0], [0, 0, 1, 1]]]', [[[1, 1, 0, 0], [0, 1, 1, 0], [0, 0, 1, 1]]], [[1, 0, 6, 0, 1], 2]], ['control [[[1, 0, 1, 1, 0], [0, 1, 1, 1, 1]]]', [[[1, 0, 1, 1, 0], [0, 1, 1, 1, 1]]], [[1, 0, 0, 2, 1, 0], 3]]]]\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-weight-distribution-minimum-weight","generated_at":"2026-09-29T14:48:37.279988+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Code designers use weight enumerators to estimate undetected-error probability and minimum distance.","root_cause":"dmin is computed from the generator rows rather than from all nonzero codewords.","sha256":"24965b26dc003731a3011afbef3be0ff95703277a824b7395a6d79472d8a0047","title":"Weight distribution takes the minimum row weight as the distance · 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":40.703,"exit_code":1,"observations":[{"actual":[[2,2,4,4,2,2],0],"check":"regression [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]]","expected":[[2,2,4,4,2,2],1],"passed":false},{"actual":[[1,1,6,6,1,1,0,0],0],"check":"regression [[[0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, ...","expected":[[1,1,6,6,1,1,0,0],1],"passed":false},{"actual":[[1,0,0,7,7,0,0,1],0],"check":"partial-repair [[[1, 0, 0, 0, 1, 1, 0], [0, 1, 0, 0, 1, 0, 1], [0, 0, 1, 0, 0, 1, ...","expected":[[1,0,0,7,7,0,0,1],3],"passed":false},{"actual":[[1,0,0,1],0],"check":"partial-repair [[[1, 1, 1]]]","expected":[[1,0,0,1],3],"passed":false},{"actual":[[2,0,0,0],0],"check":"control [[[0, 0, 0]]]","expected":[[2,0,0,0],0],"passed":true},{"actual":[[1,0,6,0,1],0],"check":"control [[[1, 1, 0, 0], [0, 1, 1, 0], [0, 0, 1, 1]]]","expected":[[1,0,6,0,1],2],"passed":false},{"actual":[[1,0,0,2,1,0],0],"check":"control [[[1, 0, 1, 1, 0], [0, 1, 1, 1, 1]]]","expected":[[1,0,0,2,1,0],3],"passed":false},{"actual":[[2,0,2,0],0],"check":"control [[[1, 1, 0], [1, 1, 0]]]","expected":[[2,0,2,0],2],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]]\", \"actual\": [[2, 2, 4, 4, 2, 2], 0], \"expected\": [[2, 2, 4, 4, 2, 2], 1], \"passed\": false}, {\"check\": \"regression [[[0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, ...\", \"actual\": [[1, 1, 6, 6, 1, 1, 0, 0], 0], \"expected\": [[1, 1, 6, 6, 1, 1, 0, 0], 1], \"passed\": false}, {\"check\": \"partial-repair [[[1, 0, 0, 0, 1, 1, 0], [0, 1, 0, 0, 1, 0, 1], [0, 0, 1, 0, 0, 1, ...\", \"actual\": [[1, 0, 0, 7, 7, 0, 0, 1], 0], \"expected\": [[1, 0, 0, 7, 7, 0, 0, 1], 3], \"passed\": false}, {\"check\": \"partial-repair [[[1, 1, 1]]]\", \"actual\": [[1, 0, 0, 1], 0], \"expected\": [[1, 0, 0, 1], 3], \"passed\": false}, {\"check\": \"control [[[0, 0, 0]]]\", \"actual\": [[2, 0, 0, 0], 0], \"expected\": [[2, 0, 0, 0], 0], \"passed\": true}, {\"check\": \"control [[[1, 1, 0, 0], [0, 1, 1, 0], [0, 0, 1, 1]]]\", \"actual\": [[1, 0, 6, 0, 1], 0], \"expected\": [[1, 0, 6, 0, 1], 2], \"passed\": false}, {\"check\": \"control [[[1, 0, 1, 1, 0], [0, 1, 1, 1, 1]]]\", \"actual\": [[1, 0, 0, 2, 1, 0], 0], \"expected\": [[1, 0, 0, 2, 1, 0], 3], \"passed\": false}, {\"check\": \"control [[[1, 1, 0], [1, 1, 0]]]\", \"actual\": [[2, 0, 2, 0], 0], \"expected\": [[2, 0, 2, 0], 2], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":40.671,"exit_code":1,"observations":[{"actual":[[2,2,4,4,2,2],2],"check":"regression [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]]","expected":[[2,2,4,4,2,2],1],"passed":false},{"actual":[[1,1,6,6,1,1,0,0],2],"check":"regression [[[0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, ...","expected":[[1,1,6,6,1,1,0,0],1],"passed":false},{"actual":[[1,0,0,7,7,0,0,1],3],"check":"partial-repair [[[1, 0, 0, 0, 1, 1, 0], [0, 1, 0, 0, 1, 0, 1], [0, 0, 1, 0, 0, 1, ...","expected":[[1,0,0,7,7,0,0,1],3],"passed":true},{"actual":[[1,0,0,1],3],"check":"partial-repair [[[1, 1, 1]]]","expected":[[1,0,0,1],3],"passed":true},{"actual":[[2,0,0,0],0],"check":"control [[[0, 0, 0]]]","expected":[[2,0,0,0],0],"passed":true},{"actual":[[1,0,6,0,1],2],"check":"control [[[1, 1, 0, 0], [0, 1, 1, 0], [0, 0, 1, 1]]]","expected":[[1,0,6,0,1],2],"passed":true},{"actual":[[1,0,0,2,1,0],3],"check":"control [[[1, 0, 1, 1, 0], [0, 1, 1, 1, 1]]]","expected":[[1,0,0,2,1,0],3],"passed":true},{"actual":[[2,0,2,0],2],"check":"control [[[1, 1, 0], [1, 1, 0]]]","expected":[[2,0,2,0],2],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]]\", \"actual\": [[2, 2, 4, 4, 2, 2], 2], \"expected\": [[2, 2, 4, 4, 2, 2], 1], \"passed\": false}, {\"check\": \"regression [[[0, 0, 0, 1, 0, 1, 1], [1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, ...\", \"actual\": [[1, 1, 6, 6, 1, 1, 0, 0], 2], \"expected\": [[1, 1, 6, 6, 1, 1, 0, 0], 1], \"passed\": false}, {\"check\": \"partial-repair [[[1, 0, 0, 0, 1, 1, 0], [0, 1, 0, 0, 1, 0, 1], [0, 0, 1, 0, 0, 1, ...\", \"actual\": [[1, 0, 0, 7, 7, 0, 0, 1], 3], \"expected\": [[1, 0, 0, 7, 7, 0, 0, 1], 3], \"passed\": true}, {\"check\": \"partial-repair [[[1, 1, 1]]]\", \"actual\": [[1, 0, 0, 1], 3], \"expected\": [[1, 0, 0, 1], 3], \"passed\": true}, {\"check\": \"control [[[0, 0, 0]]]\", \"actual\": [[2, 0, 0, 0], 0], \"expected\": [[2, 0, 0, 0], 0], \"passed\": true}, {\"check\": \"control [[[1, 1, 0, 0], [0, 1, 1, 0], [0, 0, 1, 1]]]\", \"actual\": [[1, 0, 6, 0, 1], 2], \"expected\": [[1, 0, 6, 0, 1], 2], \"passed\": true}, {\"check\": \"control [[[1, 0, 1, 1, 0], [0, 1, 1, 1, 1]]]\", \"actual\": [[1, 0, 0, 2, 1, 0], 3], \"expected\": [[1, 0, 0, 2, 1, 0], 3], \"passed\": true}, {\"check\": \"control [[[1, 1, 0], [1, 1, 0]]]\", \"actual\": [[2, 0, 2, 0], 2], \"expected\": [[2, 0, 2, 0], 2], \"passed\": true}], \"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."}}