On the structure of the linear codes with a given automorphism

Stefka Bouyuklieva

doi:10.3934/amc.2023051

Article Contents

2024, Volume 18, Issue 2: 535-548. Doi: 10.3934/amc.2023051

This issue Previous Article Lengths of divisible codes with restricted column multiplicities Next Article Sidon sets, sum-free sets and linear codes

On the structure of the linear codes with a given automorphism

Stefka Bouyuklieva

Faculty of Mathematics and Informatics, St. Cyril and St. Methodius University of Veliko Tarnovo, Bulgaria

Received: March 2023

Revised: September 2023

Early access: November 15, 2023

Published online: November 15, 2023

The research is partially supported by [the Bulgarian National Science Fund under Contract No KP-06-H62/2/13.12.2022].

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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.

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Mathematics Subject Classification: Primary: 94B05, 20B25.

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