On the Structure of the Linear Codes with a Given Automorphism
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913220184244224 |
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| author | Bouyuklieva, Stefka |
| author_facet | Bouyuklieva, Stefka |
| contents | The purpose of this paper is to present the structure of the linear codes over a finite field with q elements that have a permutation automorphism of order m. These codes can be considered as generalized quasi-cyclic codes. Quasi-cyclic codes and almost quasi-cyclic codes are discussed in detail, presenting necessary and sufficient conditions for which linear codes with such an automorphism are self-orthogonal, self-dual, or linear complementary dual. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_05288 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Structure of the Linear Codes with a Given Automorphism Bouyuklieva, Stefka Information Theory Discrete Mathematics Combinatorics 94B05, 20B25 The purpose of this paper is to present the structure of the linear codes over a finite field with q elements that have a permutation automorphism of order m. These codes can be considered as generalized quasi-cyclic codes. Quasi-cyclic codes and almost quasi-cyclic codes are discussed in detail, presenting necessary and sufficient conditions for which linear codes with such an automorphism are self-orthogonal, self-dual, or linear complementary dual. |
| title | On the Structure of the Linear Codes with a Given Automorphism |
| topic | Information Theory Discrete Mathematics Combinatorics 94B05, 20B25 |
| url | https://arxiv.org/abs/2309.05288 |