The Automorphism Group of an Extremal [72,36,16] Code Does Not Contain Z^sub 7^, Z^sub 3^, × Z^sub 3^, or D^sub 10

A computer calculation with Magma shows that there is no extremal self-dual binary code $C$ of length 72 that has an automorphism group containing either the dihedral group of order 10, the elementary abelian group of order 9, or the cyclic group of order 7. Combining this with the known results in...

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Bibliographic Details
Published inIEEE transactions on information theory Vol. 58; no. 11; p. 6916
Main Authors Feulner, T, Nebe, G
Format Journal Article
LanguageEnglish
Published New York The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 01.11.2012
Subjects
Algebra
Codes
Coding theory
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Summary:A computer calculation with Magma shows that there is no extremal self-dual binary code $C$ of length 72 that has an automorphism group containing either the dihedral group of order 10, the elementary abelian group of order 9, or the cyclic group of order 7. Combining this with the known results in the literature, one obtains that the order of ${rm Aut}(C)$ is either 5 or divides 24. [PUBLICATION ABSTRACT]
ISSN:0018-9448
1557-9654