Linear codes resulting from finite group actions

Document Type : Research Paper


Department of Mathematics, University of Cadi Ayyad, Box 63 46000 Route Sidi Bouzid, Safi, Morocco


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.


Main Subjects

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Volume 11, Issue 4 - Serial Number 4
December 2022
Pages 335-343
  • Receive Date: 29 November 2020
  • Revise Date: 29 December 2021
  • Accept Date: 14 January 2022
  • Published Online: 01 December 2022