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Linear codes resulting from finite group actions | ||
| Transactions on Combinatorics | ||
| مقاله 8، دوره 11، شماره 4، اسفند 2022، صفحه 335-343 اصل مقاله (472.79 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2022.126254.1786 | ||
| نویسنده | ||
| Driss Harzalla* | ||
| Department of Mathematics, University of Cadi Ayyad, Box 63 46000 Route Sidi Bouzid, Safi, Morocco | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Linear Code automorphism؛ Group Actions؛ Hamming codes؛ simplex codes | ||
| مراجع | ||
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