linear codes resulting from finite group actions

In this article, we use group action theory to define some important ternary linear codes. some of these codes are self-orthogonal having a minimum distance achieving the lower bound in the previous records. then, we define two new codes sharing the same automorphism group isomorphic to c2 × m11 where m11 is the sporadic mathieu group and c2 is a cyclic group of two elements. we also study the natural action of the general linear group gl(k, 2) on the vector space f^k 2 to characterize hamming codes hk(2) and their automorphism group.