$\mathbb{F}_{p^{m}}\mathbb{F}_{p^{m}}{[u^2]}$-additive skew cyclic codes of length $2p^s $

Roghayeh Mohammadi Hesari; Mahboubeh Hosseinabadi; Rashid Rezaei; Karim Samei

doi:10.3934/amc.2022023

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2022. Doi: 10.3934/amc.2022023

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$\mathbb{F}_{p^{m}}\mathbb{F}_{p^{m}}{[u^2]}$-additive skew cyclic codes of length $2p^s $

1.
Department of Mathematics, Malayer University, Malayer, Iran
2.
Department of Mathematics, Bu Ali Sina University, Hamedan, Iran

^*Corresponding author: Rashid Rezaei
^*Corresponding author: Rashid Rezaei

Received: August 31, 2021

Revised: December 31, 2021

Early access: April 2022

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Abstract

In this paper, we first study the skew cyclic codes of length $ p^s $ over $ R_3 = \mathbb{F}_{p^m}+u\mathbb{F}_{p^m}+u^2\mathbb{F}_{p^m}, $ where $ p $ is a prime number and $ u^3 = 0. $ Then we characterize the algebraic structure of $ \mathbb{F}_{p^{m}}\mathbb{F}_{p^{m}}[u^2] $-additive skew cyclic codes of length $ 2p^s. $ We will show that there are sixteen different types of these codes and classify them in terms of their generators.

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Mathematics Subject Classification: Primary: 94B15, 16S36.

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