@article {
author = {Harzalla, Driss},
title = {Linear codes resulting from finite group actions},
journal = {Transactions on Combinatorics},
volume = {11},
number = {4},
pages = {335-343},
year = {2022},
publisher = {University of Isfahan},
issn = {2251-8657},
eissn = {2251-8665},
doi = {10.22108/toc.2022.126254.1786},
abstract = {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.},
keywords = {Linear Code automorphism,Group Actions,Hamming codes,simplex codes},
url = {https://toc.ui.ac.ir/article_26249.html},
eprint = {https://toc.ui.ac.ir/article_26249_cef63884ba688f96468d5abf3cb393bb.pdf}
}