Document Type
Lecture
Publication Date
4-1-2015
Abstract
In a recent ArXiV posting, Muzychuk noticed a relationship between the isomorphism problem for Cayley digraphs of a group G and the isomorphism problem for codes permutation invariant under G. For cyclic groups, he showed that in fact the permutation isomorphism problem for cyclic codes reduces to the isomorphism problem for circulant digraphs. This latter problem has been completely solved, and so Muzychuk produced a solution to the permutation isomorphism problem for cyclic codes. We consider the problem of computing the automorphism group of cyclic codes (and codes invariant under other groups as well). We rst give a su cient condition to decompose a code C into two subcodes C1 and C2, both invariant under the permutation automorphism group of C, and which are determined by codes codes of smaller length. Additionally, we show that PAut(C) = PAut(C1) PAut(C2). This su cient condition corresponds to an existing su cient condition that gives a similar decomposition of a vertex-transitive digraph. We then use this to determine strong constraints on the permutation automorphism groups of cyclic codes of length pq, where p and q are prime. This is joint work with Mikhail Muzychuk of Netanya Academic College.
Relational Format
presentation
Recommended Citation
Dobson, Ted, "Automorphism groups of codes" (2015). Combinatorics Seminar. 38.
https://egrove.olemiss.edu/math_combinatorics/38
