On the binary codes with parameters of triply-shortened 1-perfect codes
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Publication:438873
DOI10.1007/s10623-011-9574-1zbMath1272.94094arXiv1104.0005OpenAlexW3100598789MaRDI QIDQ438873
Publication date: 31 July 2012
Published in: Designs, Codes and Cryptography (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1104.0005
weight distributionHamming codecoding theoryequitable partitionperfect coloringdistance distribution1-perfect codeextended codetriply-shortened 1-perfect code
Related Items (6)
Perfect 2‐colorings of Hamming graphs ⋮ Perfect colorings of the infinite square grid: coverings and twin colors ⋮ On calculation of the interweight distribution of an equitable partition ⋮ The extended 1-perfect trades in small hypercubes ⋮ On the \(\mathrm{OA}(1536,13,2,7)\) and related orthogonal arrays ⋮ Harmonic Distributions for Equitable Partitions of a Hypercube
Cites Work
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- On weight distributions of perfect colorings and completely regular codes
- The triply shortened binary Hamming code is optimal
- Two optimal one-error-correcting codes of length 13 that are not doubly shortened perfect codes
- On the binary codes with parameters of doubly-shortened 1-perfect codes
- Every binary (2/sup m/-2, 2/sup 2(m)-2-m/, 3) code can be lengthened to form a perfect code of length 2/sup m/-1
- On Optimal Binary One-Error-Correcting Codes of Lengths $2^{m}-4$ and $2^{m}-3$
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