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 C_۲ \times M_{۱۱} where M_{۱۱} is the Sporadic Mathieu group and C_{۲} is a cyclic group of two elements. We also study the natural action of the general linear group GL (k, ۲) on the vector space F_۲ ^ k to characterize Hamming codes H_k (۲) and their automorphism group.

کلیدواژه ها:

Linear Code automorphism ، Group Actions ، Hamming codes ، simplex codes