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Skew cyclic codes over a finite non-chain ring and an application

Cruz Mohan Corresponding Author
Department of Mathematics, Bishop Heber College, Tiruchirappalli - 620 017, Tamil Nadu, India
ROR
Karthick Gowdhaman
Department of Mathematics, SASTRA Deemed University, Thanjavur-613401, Tamil Nadu, India
ROR
Gokul Radhakrishnan
Department of Mathematics, Bharathidasan University, Tiruchirappalli - 620 024, Tamil Nadu, India
ROR
Durairajan Chinnapillai
Durairajan Chinnapillai;Department of Mathematics, Bharathidasan University, Tiruchirappalli, Tamil Nadu, India
ROR
Irfan Siap
Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, Al Khobar 31952, Saudi Arabia
ROR
https://doi.org/10.13069/jacodesmath.v13i2.453
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Abstract

This article studies \( \Theta_t \)-cyclic and \( (\Theta_t,\lambda) \)-constacyclic codes over the finite commutative non-chain Frobenius ring

\[ R = \mathbb{F}_q[u,v,w]/\langle u^2-u,\ v^2-v,\ w^2-1,\ uv,\ uw-wu,\ wv-vw \rangle .\]

Gray maps, structural decompositions, and generator descriptions are developed for both odd- and even-characteristic cases. The paper further determines principal generators in the associated skew polynomial rings, dual codes, idempotent generators, and conditions for self-duality. It also presents explicit examples over specific finite fields and extends the framework to DNA codes in the even-characteristic setting through reversibility and complement constraints. Spanning sets, cardinality formulas, and optimal DNA-code constructions meeting the Griesmer bound are also obtained.

Received: 12 September 2025 | Accepted: 05 April 2026

Keywords
Linear codes $\Theta_t$-cyclic codes Non-chain rings Gray maps $(\Theta_t,\lambda)$-constacyclic codes DNA-codes

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References

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Vol. 13 Issue 2 : May 2026
Articles
English
pp. 253-271
Received 07 April 2026
Published 06 May 2026

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How to Cite

Mohan, C. ., Gowdhaman, K., Radhakrishnan, G. ., Chinnapillai, D. ., & Siap, I. . (2026). Skew cyclic codes over a finite non-chain ring and an application . Journal of Algebra Combinatorics Discrete Structures and Applications, 13(2), 253–271. https://doi.org/10.13069/jacodesmath.v13i2.453
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Copyright (c) 2026 Cruz Mohan, Karthick Gowdhaman, Gokul Radhakrishnan, Durairajan Chinnapillai, Irfan Siap
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