Linear codes resulting from finite group actions
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...
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| Format: | Article |
| Language: | English |
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University of Isfahan
2022-12-01
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| Series: | Transactions on Combinatorics |
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| Online Access: | https://toc.ui.ac.ir/article_26249_cef63884ba688f96468d5abf3cb393bb.pdf |
| Summary: | 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. |
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| ISSN: | 2251-8657 2251-8665 |