The Automorphism Group of a Self Dual Binary [72,36,16] Code Does Not Contain Z4

Abstract

It has been proven in a series of works that the order of the automorphism group of a binary [72,36,16] code does not exceed five. We obtain a parametrization of all self-dual binary codes of length 72 with automorphism of order 4 which can be extremal. We use extensive computations in MAGMA and on a supercomputer to show that an extremal binary code of length 72 does not have an element of order 4.

arXiv comment10 pages; references added; typos corrected; section 4 expanded

References in corpus (1)

• The automorphism group of a self-dual [72,36,16] code does not contain S_3, A_4, or D_8