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- Title
Structure of F<sub>q</sub>R-linear (Θ, Δ<sub>Θ</sub>)-cyclic codes.
- Authors
Patel, Shikha; Singh, Ashutosh; Prakash, Om
- Abstract
Let Fq be the finite field of order q = pm where p is a prime, and m is a positive integer. This work introduces FqR-linear (Θ, ΔΘ)-cyclic codes where R = Fq + uFq with u² = u, i.e., (Θ, ΔΘ)-cyclic codes over FqR. With the help of the decomposition method, we study the structural properties and determine the generator polynomials of FqR-linear (Θ, ΔΘ)-cyclic codes. Further, we define the Gray map over FqR and find the Gray images of FqR-linear (Θ, ΔΘ)-cyclic codes over Fq. Finally, with the help of our established results, we have constructed some new codes corresponding to FqR-linear (Θ, ΔΘ)-cyclic codes.
- Subjects
CYCLIC codes; FINITE fields; DECOMPOSITION method; LINEAR codes; POLYNOMIAL rings; POLYNOMIALS
- Publication
Computational & Applied Mathematics, 2024, Vol 43, Issue 3, p1
- ISSN
0101-8205
- Publication type
Article
- DOI
10.1007/s40314-024-02631-8