Skew cyclic codes over a finite non-chain ring and an application
DOI:
https://doi.org/10.13069/jacodesmath.v13i2.453Keywords:
Linear codes, $\Theta_t$-cyclic codes, Non-chain rings, Gray maps, $(\Theta_t,\lambda)$-constacyclic codes, DNA-codesAbstract
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
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