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.
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}
}