On the automorphism group of a binary self-dual $$[120, 60, 24]$$ [ 120 , 60 , 24 ] code
نویسندگان
چکیده
منابع مشابه
On the Automorphism Group of a Binary Self-dual [120, 60, 24] Code
We prove that an automorphism of order 3 of a putative binary self-dual [120, 60, 24] code C has no fixed points. Moreover, the order of the automorphism group of C divides 2a ·3 ·5 ·7 ·19 ·23 ·29 with a ∈ N0. Automorphisms of odd composite order r may occur only for r = 15, 57 or r = 115 with corresponding cycle structures 3·5-(0, 0, 8; 0), 3 · 19-(2, 0, 2; 0) or 5 · 23-(1, 0, 1; 0) respective...
متن کاملSome new results on the self-dual [120, 60, 24] code
The existence of an extremal self-dual binary linear code of length 120 is a long-standing open problem. We continue the investigation of its automorphism group, proving that automorphisms of order 30 and 57 cannot occur. Supposing the involutions acting fixed point freely, we show that also automorphisms of order 8 cannot occur and the automorphism group is of order at most 120, with further r...
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We prove that the automorphism group of a binary self-dual doubly-even [72, 36, 16] code has order 5, 7, 10, 14 or d where d divides 18 or 24, or it is A4 × C3.
متن کاملAutomorphism of order 2p in binary self-dual extremal codes of length a multiple of 24
Automorphisms of order 2p in binary self-dual extremal codes of length a multiple of 24 Abstract Let C be a binary self-dual code with an automorphism g of order 2p, where p is an odd prime, such that g p is a fixed point free involution. If C is extremal of length a multiple of 24 all the involutions are fixed point free, except the Golay Code and eventually putative codes of length 120. Conne...
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The purpose of this paper is to complete the classification of binary self-dual [48, 24, 10] codes with an automorphism of odd prime order. We prove that if there is a self-dual [48, 24, 10] code with an automorphism of type p-(c, f) with p being an odd prime, then p = 3, c = 16, f = 0. By considering only an automorphism of type 3-(16, 0), we prove that there are exactly 264 inequivalent self-...
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ژورنال
عنوان ژورنال: Applicable Algebra in Engineering, Communication and Computing
سال: 2013
ISSN: 0938-1279,1432-0622
DOI: 10.1007/s00200-013-0193-0