{
  "slug": "hamming-distance",
  "term": "Hamming distance",
  "aliases": [
    "Hamming metric"
  ],
  "definition": "Hamming distance counts the symbol positions in which two equal-length sequences differ.",
  "note": "For a binary code, minimum distance is the smallest number of bit inversions separating any two distinct codewords; it defines a guaranteed detection bound, not an observed error rate. [koopman04] Hesela's exhaustive four-bit example drops from distance three to two when the data length increases from eleven to twelve bits. [hesela-crc]",
  "status": "shipping",
  "advantages": [],
  "limitations": [],
  "related": [
    "cyclic-redundancy-check",
    "crc32c",
    "crc-burst-error",
    "error-and-erasure-decoding"
  ],
  "supersedes": [],
  "supersededBy": [],
  "firstSeen": null,
  "lastSeen": null,
  "citations": [
    {
      "id": "koopman04",
      "title": "Koopman and Chakravarty. CRC Polynomial Selection For Embedded Networks. DSN 2004, sections 2-4",
      "url": "https://users.ece.cmu.edu/~koopman/roses/dsn04/koopman04_crc_poly_embedded.pdf",
      "accessed": "2026-10-18"
    },
    {
      "id": "hesela-crc",
      "title": "Hesela: CRC polynomials, constructed error patterns and exact small-code enumeration",
      "url": "https://hesela.com/analyses/crc-polynomials-error-patterns/",
      "accessed": "2026-10-18"
    }
  ],
  "updated": "2026-10-18"
}