{
  "slug": "systematic-code",
  "term": "Systematic code",
  "aliases": [
    "Systematic encoding"
  ],
  "definition": "A systematic code includes the original data symbols unchanged among its encoded symbols.",
  "note": "In a generator-matrix representation this can be expressed by an identity block. Systematic layout alone does not imply MDS recovery: Hesela's GF(7) enumeration contains a systematic non-MDS counterexample. It is a teaching calculation, not a production codec. [hesela-matrix]",
  "status": "shipping",
  "advantages": [],
  "limitations": [
    "An identity block does not prove that arbitrary surviving rows form an invertible recovery matrix."
  ],
  "related": [
    "maximum-distance-separable-code",
    "reed-solomon-code",
    "erasure-coding"
  ],
  "supersedes": [],
  "supersededBy": [],
  "firstSeen": null,
  "lastSeen": null,
  "citations": [
    {
      "id": "rfc5510",
      "title": "Lacan, Roca, Peltotalo and Peltotalo. RFC 5510 (2009), sections 3.1, 8.2-8.4: systematic encoding and the erasure-channel assumption.",
      "url": "https://www.rfc-editor.org/rfc/rfc5510.html",
      "accessed": "2026-10-13"
    },
    {
      "id": "hesela-matrix",
      "title": "Hesela: Reed-Solomon recovery needs more than a fragment count (synthetic exact arithmetic)",
      "url": "https://hesela.com/analyses/reed-solomon-matrix-recovery-guarantees/",
      "accessed": "2026-10-13"
    }
  ],
  "updated": "2026-10-13"
}