English

On the Structure of the Linear Codes with a Given Automorphism

Information Theory 2024-02-05 v1 Discrete Mathematics Combinatorics math.IT

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.

Keywords

Cite

@article{arxiv.2309.05288,
  title  = {On the Structure of the Linear Codes with a Given Automorphism},
  author = {Stefka Bouyuklieva},
  journal= {arXiv preprint arXiv:2309.05288},
  year   = {2024}
}
R2 v1 2026-06-28T12:17:45.669Z