Additive skew polycyclic codes over $ \mathbb{F}_{p^2} $

Nuh Aydin; Amina Delhoum

doi:10.3934/amc.2025027

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2026, Volume 20: 42-51. Doi: 10.3934/amc.2025027

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Additive skew polycyclic codes over $ \mathbb{F}_{p^2} $

Nuh Aydin^1, and
Amina Delhoum^2, ,

1.
Department of Mathematics and Statistics, Kenyon College, USA
2.
LATN Laboratory, Department of Mathematics, University of Science and Technology Houari Boumediene, Algeria

^*Corresponding author: Amina Delhoum
^*Corresponding author: Amina Delhoum

Received: January 2025

Revised: May 2025

Early access: June 9, 2025

Published online: June 9, 2025

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Abstract

In this paper we investigate additive skew polycyclic codes over $ \mathbb{F}_{p^2} $, where $ p $ is a prime. We study the structure and the generator polynomials of these codes when they are induced by a vector in $ \mathbb{F}_{p}^{n} $ and in $ \mathbb{F}_{p^2}^{n} $. Our work includes a characterization of additive skew bi-polycyclic codes over $ \mathbb{F}_{4} $. Further, we give a relationship between additive skew polycyclic codes and additive sequential codes. Additionally, we present examples of additive skew polycyclic codes with more codewords than any comparable linear codes, even optimal linear codes, of the same length and the minimum weight.

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Mathematics Subject Classification: Primary: 94B15, 94B60; Secondary: 11T71.

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References

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