On rank and kernel of some mixed perfect codes

Fabio Pasticci; Thomas Westerbäck

doi:10.1016/j.disc.2008.06.037

On rank and kernel of some mixed perfect codes

Fabio Pasticci, Thomas Westerbäck^*

^*Corresponding author for this work

Not published at Aalto University

Research output: Contribution to journal › Article › Scientific › peer-review

Abstract

Mixed perfect 1-error correcting codes and the associated dual codes over the group Z (n, l), Z (n, l) = under(under(Z₂ × Z₂ × ⋯ × Z₂, {presentation form for vertical right curly bracket}), n) × underover(Z, 2, l), n ≥ 1 and l ≥ 2, are investigated. A lower and an upper bound for the rank k of the kernel of mixed perfect 1-error correcting codes in Z (n, l), depending on the rank r of the mixed perfect code and the structure of the corresponding dual code, are given. Due to a general construction of mixed perfect 1-error correcting group codes in Z (n, l), we show that the upper bound is tight for some n, l and r.

Original language	English
Pages (from-to)	2763-2774
Number of pages	12
Journal	Discrete Mathematics
Volume	309
Issue number	9
DOIs	https://doi.org/10.1016/j.disc.2008.06.037
Publication status	Published - 6 May 2009
MoE publication type	A1 Journal article-refereed

Keywords

Fourier coefficient
Mixed perfect code
Rank

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10.1016/j.disc.2008.06.037

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AB - Mixed perfect 1-error correcting codes and the associated dual codes over the group Z (n, l), Z (n, l) = under(under(Z2 × Z2 × ⋯ × Z2, {presentation form for vertical right curly bracket}), n) × underover(Z, 2, l), n ≥ 1 and l ≥ 2, are investigated. A lower and an upper bound for the rank k of the kernel of mixed perfect 1-error correcting codes in Z (n, l), depending on the rank r of the mixed perfect code and the structure of the corresponding dual code, are given. Due to a general construction of mixed perfect 1-error correcting group codes in Z (n, l), we show that the upper bound is tight for some n, l and r.

KW - Fourier coefficient

KW - Mixed perfect code

KW - Rank

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M3 - Article

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JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

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ER -

On rank and kernel of some mixed perfect codes

Abstract

Keywords

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