%0 Journal Article
%T Linear codes resulting from finite group actions
%J Transactions on Combinatorics
%I University of Isfahan
%Z 2251-8657
%A Harzalla, Driss
%D 2022
%\ 12/01/2022
%V 11
%N 4
%P 335-343
%! Linear codes resulting from finite group actions
%K Linear Code automorphism
%K Group Actions
%K Hamming codes
%K simplex codes
%R 10.22108/toc.2022.126254.1786
%X 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 $C_2 \times M_{11}$ where $M_{11}$ is the Sporadic Mathieu group and $C_{2}$ 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 $F_2 ^ k$ to characterize Hamming codes $H_k (2) $ and their automorphism group.
%U https://toc.ui.ac.ir/article_26249_cef63884ba688f96468d5abf3cb393bb.pdf