Abstract
We introduce and discuss an elementary tool from representation theory of finite groups for constructing linear codes invariant under a given permutation group G. The tool gives theoretical insight as well as a recipe for computations of generator matrices and weight distributions. In some interesting cases a classification of code vectors under the action of G can be obtained. As an explicit example a class of binary codes is studied extensively which is closely related to the class of binary codes associated to triangular graphs. A second explicit application is related to the action of the Mathieu simple group M24 on the set of octads giving many binary codes of length 759 with interesting properties. We also obtain new alternative proofs for several other theorems and construct several new codes invariant under various subgroups of the Conway simple group Co1.
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