Pentacode[1]
Description
Nonlinear \((5,40,4)_{\mathbb{Z}_4}\) code over \(\mathbb{Z}_4\) whose codewords are all cyclic permutations and negations of the strings \(01112\), \(03110\), \(21310\), and \(21132\).
Parents
Cousin
- Best \((10,40,4)\) code — Codewords of the Best code can be obtained by applying the Gray map to the pentacode [2; Sec. 2].
References
- [1]
- J. H. Conway and N. J. A. Sloane, “Quaternary constructions for the binary single-error-correcting codes of Julin, Best and others”, Designs, Codes and Cryptography 4, 31 (1994) DOI
- [2]
- J. H. Conway and N. J. A. Sloane, “Quaternary constructions for the binary single-error-correcting codes of Julin, Best and others”, Designs, Codes and Cryptography 4, 31 (1994) DOI
Page edit log
- Victor V. Albert (2023-11-22) — most recent
Cite as:
“Pentacode”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/pentacode