{
  "schemaVersion": "1.0.0",
  "kind": "synthetic-exhaustive-enumeration",
  "field": "GF(7)",
  "k": 3,
  "n": 6,
  "paritySymbols": 3,
  "generatedOn": "2026-10-13",
  "method": "Invert every 3-row subset of two explicit 6x3 matrices using exact arithmetic modulo 7.",
  "limits": "These are selected teaching constructions, not ISA-L, Ceph, RFC 5510 conformance, a reproduction of Plank-Ding, a hardware test, or a failure probability.",
  "rows": [
    {
      "id": "identity-plus-powers",
      "label": "Identity plus power rows",
      "generator": [
        [
          1,
          0,
          0
        ],
        [
          0,
          1,
          0
        ],
        [
          0,
          0,
          1
        ],
        [
          1,
          1,
          1
        ],
        [
          1,
          2,
          4
        ],
        [
          1,
          6,
          1
        ]
      ],
      "checked": 20,
      "recoverable": 19,
      "singular": [
        [
          1,
          3,
          5
        ]
      ]
    },
    {
      "id": "systematic-vandermonde",
      "label": "Whole-matrix systematic transform",
      "generator": [
        [
          1,
          0,
          0
        ],
        [
          0,
          1,
          0
        ],
        [
          0,
          0,
          1
        ],
        [
          1,
          4,
          3
        ],
        [
          3,
          6,
          6
        ],
        [
          6,
          6,
          3
        ]
      ],
      "checked": 20,
      "recoverable": 20,
      "singular": []
    }
  ],
  "counterexample": {
    "survivors": [
      1,
      3,
      5
    ],
    "dataA": [
      0,
      0,
      0
    ],
    "dataB": [
      1,
      0,
      6
    ],
    "observedA": [
      0,
      0,
      0
    ],
    "observedB": [
      0,
      0,
      0
    ]
  },
  "modelSha256": "017a055816f118fc24b4c577c7eb0a2ea301eea4ff51e792783827a77173418c",
  "analysis": "https://hesela.com/analyses/reed-solomon-matrix-recovery-guarantees/"
}