Vasilyev code[1]
Description
Member of an infinite \((2^{m+1}-1,2^{2n-m},3)\) family of perfect nonlinear codes for any \(m \geq 3\). Constructed by applying a modification of the \((u|u+v)\) construction to a perfect \((2^m-1,2^{n-m},3)\) code, not necessarily linear [2; pg. 77].
The automorphism group of these codes is always nontrivial [3].
Parents
- Binary code
- \((u|u+v)\)-construction code
- Perfect binary code — Vasilyev codes are perfect nonlinear binary codes and are inequivalent to any linear code.
- Small-distance block code
References
- [1]
- J. L. Vasilyev On nongroup close-packed codes (in Russian), Probl. Kibernet., 8 (1962), 337-339, translated in Probleme der Kibernetik 8 (1965), 375-378.
- [2]
- F. J. MacWilliams and N. J. A. Sloane. The theory of error correcting codes. Elsevier, 1977.
- [3]
- S. V. Avgustinovich, F. I. Solov’eva, and O. Heden, “On the Structure of Symmetry Groups of Vasil’ev Codes”, Problems of Information Transmission 41, 105 (2005) DOI
Page edit log
- Victor V. Albert (2023-03-31) — most recent
Cite as:
“Vasilyev code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/vasilyev