error-syndrome · shipping · also Syndrome (error-correcting codes), ECC syndrome

Error syndrome

An error syndrome is the result of applying a linear code's parity-check equations to a received word.

Related Observatory article: Error syndrome on hesela.com

With parity-check matrix H and received word r, the syndrome is H r^T over the code's field. Zero indicates code membership, not identity with the originally stored word; different error patterns can share a syndrome. [1]

Linux v6.12 bch_decode can accept precomputed syndromes and returns located-error counts or error codes. It does not correct the input buffer itself. Located errors may be in payload or ECC: only locations below 8 * len select payload bits to flip. A returned count is not an unconditional physical error count relative to the original word. [2]

Relations

related
Error-correcting code, Codeword (storage ECC), BCH code, Hamming distance, LDPC (NAND ECC)

Citations

  1. H. C. A. van Tilborg: Coding Theory, a First Course, sections 2.1-2.2 and 4.2 (accessed 2026-10-25)
  2. Linux v6.12 lib/bch.c: bch_decode return values, caller correction and syndrome processing (accessed 2026-10-25)

Further reading

  1. Hesela: BCH, LDPC and the RBER aggregation trap, decoder contracts (accessed 2026-10-25)

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Hesela team. Error syndrome. Hesela. 2026-10-25. https://hesela.dev/terms/error-syndrome/