On automorphism groups of binary linear codes
Martino Borello · Contemporary mathematics - American Mathematical Society · 2015
Let C \mathcal {C} be a binary linear code and suppose that its automorphism group contains a non trivial subgroup G G . What can we say about C \mathcal {C} knowing G G ? In this paper we collect some answers to this question in the cases G ≅ C p G\cong C_p , G ≅ C 2 p G\cong C_{2p} and G ≅ D 2 p G\cong D_{2p} ( p p an odd prime), with a particular regard to the case in which C \mathcal {C} is self-dual. Furthermore we generalize some methods used in other papers on this subject. Finally we give a short survey on the problem of determining the automorphism group of a putative self-dual [ 72 , 36 , 16 ] [72,36,16] code, in order to show where these methods can be applied.