| 1. |
- Heden, Olof, et al.
(författare)
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ON THE EXISTENCE OF EXTENDED PERFECT BINARY CODES WITH TRIVIAL SYMMETRY GROUP
- 2009
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Ingår i: Advances in Mathematics of Communications. - : American Institute of Mathematical Sciences (AIMS). - 1930-5346 .- 1930-5338. ; 3:3, s. 295-309
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Tidskriftsartikel (refereegranskat)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 = 2(m) - 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.
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| 2. |
- Heden, Olof, et al.
(författare)
-
on the symmetry group of extended perfect binary codes of length n+1 and rank n-log(n+1)+2
- 2012
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Ingår i: Advances in Mathematics of Communication. - : American Institute of Mathematical Sciences (AIMS). - 1930-5346 .- 1930-5338. ; 6:2, s. 121-130
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Tidskriftsartikel (refereegranskat)abstract
- It is proved that for every integer n = 2(k) - 1, with k >= 5, there exists a perfect code C of length n, of rank r = n - log(n + 1) + 2 and with a trivial symmetry group. This result extends an earlier result by the authors that says that for any length n = 2(k) - 1, with k >= 5, and any rank r, with n - log(n + 1) + 3 <= r <= n - 1 there exist perfect codes with a trivial symmetry group.
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