Abstract
The set of permutations of the coordinate set that maps a perfect code C into itself is called the symmetry group of C and is denoted by Sym(C). It is proved that for all integers n = 2m - 1, where m = 4, 5, 6, . . . , and for any integer r, where n - log(n + 1) + 3≤ r≤ n - 1, there are perfect codes of length n and rank r with a trivial symmetry group, i.e. Sym(C) = {id}. The result is shown to be true, more generally, for the extended perfect codes of length n + 1.
Original language | English |
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Pages (from-to) | 295-309 |
Number of pages | 15 |
Journal | Advances in Mathematics of Communications |
Volume | 3 |
Issue number | 3 |
DOIs | |
Publication status | Published - Aug 2009 |
MoE publication type | A1 Journal article-refereed |
Keywords
- Perfect codes
- Symmetry group