University of IsfahanTransactions on Combinatorics2251-865711420221201Linear codes resulting from finite group actions3353432624910.22108/toc.2022.126254.1786ENDrissHarzallaDepartment of Mathematics, University of Cadi Ayyad, Box 63 46000 Route Sidi Bouzid, Safi, MoroccoJournal Article20201129In 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.https://toc.ui.ac.ir/article_26249_cef63884ba688f96468d5abf3cb393bb.pdf