Abstract
Let G be a permutation group on an n-element set Ω. We study the binary code C (G, Ω) defined as the dual code of the code spanned by the sets of fixed points of involutions of G. We show that any G-invariant self-orthogonal code of length n is contained in C (G, Ω). Many self-orthogonal codes related to sporadic simple groups, including the extended Golay code, are obtained as C (G, Ω). Some new self-dual codes invariant under sporadic almost simple groups are constructed.
Original language | English |
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Pages (from-to) | 610-621 |
Number of pages | 12 |
Journal | Journal of Algebra |
Volume | 309 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2007 Mar 15 |
Externally published | Yes |
Keywords
- Permutation group
- Self-orthogonal code and self-dual code
- Sporadic simple group
ASJC Scopus subject areas
- Algebra and Number Theory