Automorphism groups of self-dual binary linear codes with a particular regard to the extremal case of length 72
Vortrag von Dr. Martino Borello
Datum: 07.04.14 Zeit: 13.00 - 14.00 Raum:
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 talk we will show some answers to this question. We will focus on the cases in which G has order p or 2p, where p is an odd prime, and C is self-dual. We will apply our methods to the investigation of the automorphism group of a putative self-dual [72;36;16] code, whose existence is a long-standing open problem of Classical Coding Theory. We will give, retracing the work of many authors, a sketch of the proof that the order of the automorphism group of such a code is at most 5.