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 thesis we collect some answers to this question. We focus on the cases G = C_p, G = C_2p and G = D_2p (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. The third chapter is devoted to the investigation of the automorphism group of a putative self-dual [72; 36; 16] code, whose existence is a long-standing open problem. Last chapter is about semi self-dual codes and new upped bound on their dual distance.

Automorphism groups of self-dual binary linear codes with a particular regard to the extremal case of length 72

BORELLO, MARTINO
2014

Abstract

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 thesis we collect some answers to this question. We focus on the cases G = C_p, G = C_2p and G = D_2p (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. The third chapter is devoted to the investigation of the automorphism group of a putative self-dual [72; 36; 16] code, whose existence is a long-standing open problem. Last chapter is about semi self-dual codes and new upped bound on their dual distance.
16-gen-2014
Inglese
Automorphism group; extremal self-dual codes
DALLA VOLTA, FRANCESCA
Università degli Studi di Milano-Bicocca
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.14242/170108
Il codice NBN di questa tesi è URN:NBN:IT:UNIMIB-170108