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 |
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Pages (from-to) | 2763-2774 |
Number of pages | 12 |
Journal | Discrete Mathematics |
Volume | 309 |
Issue number | 9 |
DOIs | |
Publication status | Published - 6 May 2009 |
MoE publication type | A1 Journal article-refereed |
Keywords
- Fourier coefficient
- Mixed perfect code
- Rank