TY - JOUR
ID - 26249
TI - Linear codes resulting from finite group actions
JO - Transactions on Combinatorics
JA - TOC
LA - en
SN - 2251-8657
AU - Harzalla, Driss
AD - Department of Mathematics, University of Cadi Ayyad, Box 63 46000 Route Sidi Bouzid, Safi, Morocco
Y1 - 2022
PY - 2022
VL - 11
IS - 4
SP - 335
EP - 343
KW - Linear Code automorphism
KW - Group Actions
KW - Hamming codes
KW - simplex codes
DO - 10.22108/toc.2022.126254.1786
N2 - 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.
UR - https://toc.ui.ac.ir/article_26249.html
L1 - https://toc.ui.ac.ir/article_26249_cef63884ba688f96468d5abf3cb393bb.pdf
ER -