Automorphism groups of self-dual codes
نویسنده
چکیده
Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek online verfügbar.
منابع مشابه
Enumeration of the Binary Self-Dual Codes of Length 34
An (n, k) binary self-orthogonal code is an (n, k) binary linear code C that is contained in its orthogonal complement C⊥. A self-orthogonal code C is self-dual if C = C⊥. Two codes, C1 and C2, are equivalent if and only if there exists a coordinate permutation of C1 that takes C1 into C2. The automorphism group of a code C is the set of all coordinate permutations of C that takes C into itself...
متن کاملA Search for New Optimal Singly - Even Self - Dual Codes of Length 48
The best binary self-dual singly-even codes of length 48 have minimal weight 10 and are called optimal. There are 75 such codes found by Harada at al. in 2005. We use the method for constructing self-dual codes via automorphism of order three to find 102 optimal self-dual singly-even codes of length 48. We use computer algebra system Magma to construct the codes to compute their weight enumerat...
متن کاملOn the classification of the extremal self-dual codes over small fields with 2-transitive automorphism groups
There are seven binary extremal self-dual doubly-even codes which are known to have a 2-transitive automorphism group. Using representation theoretical methods we show that there are no other such codes, except possibly n = 1 024. We also classify all extremal ternary self-dual and quaternary Hermitian self-dual codes.
متن کاملOn the classification of extremal doubly even self-dual codes with 2-transitive automorphism groups
In this note, we complete the classification of extremal doubly even self-dual codes with 2-transitive automorphism groups.
متن کاملOn the automorphism groups of binary linear codes
Let C be a binary linear code and suppose that its automorphism group contains a non trivial subgroup G. What can we say about C knowing G? In this paper we collect some answers to this question in the cases G ∼= Cp, G ∼= C2p and G ∼= D2p (p an odd prime), with a particular regard to the case in which C is self-dual. Furthermore we generalize some methods used in other papers on this subject. F...
متن کاملNew results on the classification of binary self - dual [ 52 , 26 , 10 ] codes with an automorphism of odd prime order 1
The paper presents an important step toward the complete classification of all optimal binary self-dual codes of length 52 that possess an automorphism of odd prime order. Using a method for constructing and classifying binary self-dual codes with an automorphism of odd prime order p we give full classification of all [52, 26, 10] binary self-dual codes with an authomorphism of type 3-(16,4) an...
متن کامل