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Some Remarks on Self-Dual Codes Invariant Under Almost Simple Permutation Groups

Published online by Cambridge University Press:  15 April 2019

C. M. Campbell
Affiliation:
University of St Andrews, Scotland
C. W. Parker
Affiliation:
University of Birmingham
M. R. Quick
Affiliation:
University of St Andrews, Scotland
E. F. Robertson
Affiliation:
University of St Andrews, Scotland
C. M. Roney-Dougal
Affiliation:
University of St Andrews, Scotland
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Summary

We present some recent advances on the question of enumeration and classification of self-dual codes invariant under finite non-solvable permutation groups. In particular, we examine the question for almost simple groups of sporadic or rank 3 types. As a by-product we determine all doubly even and extremal codes of length n ≤ 4095 which admit an almost simple group of sporadic or rank 3 type as a permutation group of automorphisms acting transitively on the code’s coordinate positions.

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Publisher: Cambridge University Press
Print publication year: 2019

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