<abstract xmlns="http://www.w3.org/1999/xhtml">

The fundamental aim of this research is to analyze the configuration of 𝔽4<italic>R</italic> submodules, skew cyclic codes over 𝔽4<italic>R</italic> and establish their connection with DNA codes, where 𝔽4 is a field of order 4 and <italic>R</italic> = 𝔽4 + <italic>u</italic>𝔽4 + <italic>v</italic>𝔽4 + <italic>w</italic>𝔽4 with <italic>u</italic>2 = <italic>u, v</italic>2 = <italic>v, w</italic>2 = <italic>w, uv</italic> = <italic>vu</italic> = 0, <italic>vw</italic> = <italic>wv</italic> = 0, <italic>wu</italic> = <italic>uw</italic> = 0 is a finite ring. This is achieved by examining particular subclasses like reversible codes. Ultimately, this study aims to utilize Gray maps to derive codes that possess the characteristics of DNA structures. At the end of this paper, we have provided the necessary and sufficient condition for skew cyclic codes to be reversible complement.
</abstract>

The fundamental aim of this research is to analyze the configuration of 𝔽4R submodules, skew cyclic codes over 𝔽4R and establish their connection with DNA codes, where 𝔽4 is a field of order 4 and R = 𝔽4 + u𝔽4 + v𝔽4 + w𝔽4 with u2 = u, v2 = v, w2 = w, uv = vu = 0, vw = wv = 0, wu = uw = 0 is a finite ring. This is achieved by examining particular subclasses like reversible codes. Ultimately, this study aims to utilize Gray maps to derive codes that possess the characteristics of DNA structures. At the end of this paper, we have provided the necessary and sufficient condition for skew cyclic codes to be reversible complement.

Skew cyclic codes over 𝔻4<italic>R</italic> and their applications to DNA codes construction

Aligarh Muslim University, Aligarh-202002

Vignan’s Foundation for Science, Technoligy and Research

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Skew cyclic codes over 𝔻 and their applications to DNA codes construction

The fundamental aim of this research is to analyze the configuration of 𝔽4R submodules, skew cyclic codes over 𝔽4R and establish their connection with DNA...

Skew cyclic codes over 𝔻₄R and their applications to DNA codes construction

Online veröffentlicht: 10. Juli 2024

Seitenbereich: 157 - 175

Eingereicht: 24. Juni 2023

Akzeptiert: 30. Okt. 2023

DOI: https://doi.org/10.2478/auom-2024-0025

Schlüsselwörter
Cyclic codes, skew polynomial ring, DNA codes, reversible complement

© 2024 Nadeem ur Rehman et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Skew cyclic codes over 𝔻4R and their applications to DNA codes construction

Online veröffentlicht: 10. Juli 2024

Seitenbereich: 157 - 175

Eingereicht: 24. Juni 2023

Akzeptiert: 30. Okt. 2023

DOI: https://doi.org/10.2478/auom-2024-0025

SchlüsselwörterCyclic codes, skew polynomial ring, DNA codes, reversible complement

© 2024 Nadeem ur Rehman et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Skew cyclic codes over 𝔻₄R and their applications to DNA codes construction

Schlüsselwörter
Cyclic codes, skew polynomial ring, DNA codes, reversible complement