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- Title
On the structure of the linear codes with a given automorphism.
- Authors
Bouyuklieva, Stefka
- Abstract
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.
- Subjects
LINEAR codes; CYCLIC codes; FINITE fields; PERMUTATION groups; MORPHISMS (Mathematics)
- Publication
Advances in Mathematics of Communications, 2024, Vol 18, Issue 2, p1
- ISSN
1930-5346
- Publication type
Article
- DOI
10.3934/amc.2023051