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

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...

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Bibliographic Details
Published in:arXiv.org 2013-11
Main Authors: Yorgov, Vassil, Yorgov, Daniel
Format: Article
Language:English
Subjects:
Automorphisms
Binary codes
Binary system
Codes
Magma
Parameterization
Online Access:Get full text
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Summary: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.
ISSN:2331-8422