Chien-Choy generalized BCH (GBCH) code[1]
Description
An \([n,k\geq n-rm, d\geq r+1]_q\) alternant code defined using two polynomials \(P(x),G(x)\) that are relatively prime to \(x^n-1\), with \(\deg P \leq n-1\) and \(r = \deg G \leq n-1\).
See [2; Ch. 12] for the parity-check matrix.
Cousin
- Goppa code— In the binary case, GBCH\((z^{n-1},G)\) is the Goppa code \(\Gamma(L,G)\) where \(L\) consists of the \(n\)th roots of unity [2; pg. 360].
Member of code lists
Primary Hierarchy
Parents
GBCH codes are a special case of alternant codes [2; Ch. 12].
Chien-Choy generalized BCH (GBCH) code
Children
\(q\)-ary BCH codes are a special case of GBCH codes [2; Ch. 12].
Generalized Srivastava codes are a special case of GBCH codes [2; Ch. 12].
References
- [1]
- R. Chien and D. Choy, “Algebraic generalization of BCH-Goppa-Helgert codes”, IEEE Transactions on Information Theory 21, 70 (1975) DOI
- [2]
- F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes (Elsevier, 1977)
Page edit log
- Victor V. Albert (2026-06-08) — most recent
- Victor V. Albert (2024-08-18)
Cite as:
“Chien-Choy generalized BCH (GBCH) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/gbch, arXiv:2606.11484