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- Title
Gray Images of Constacyclic Codes over a Non-chain Extension of Z4.
- Authors
Mohan, Cruz; Gowdhaman, Karthick; Chinnapillai, Durairajan; Gao, Jian
- Abstract
Let Z 4 be the ring of integers modulo 4. We study the Λ -constacyclic and (θ , Λ) -cyclic codes over the non-chain ring R = Z 4 [ u , v ] / ⟨ u 2 = 1 , v 2 = 0 , u v = v u = 0 ⟩ for a unit Λ = 1 + 2 u + 2 v in R. We define several Gray maps and find that the respective Gray images of a quasi-cyclic code over Z 4 are cyclic, quasi-cyclic or permutation equivalent to this code. For an odd positive integer n , we determine the generator polynomials of cyclic and Λ -constacyclic codes of length n over R. Further, we prove that a (θ , Λ) -cyclic code of length n is a Λ -constacyclic code if n is odd, and a Λ -quasi-twisted code if n is even. A few examples are also incorporated, in which two parameters are new and one is best known to date.
- Subjects
RINGS of integers; PERMUTATIONS; LINEAR codes; POLYNOMIALS; INTEGERS; PERMUTATION groups
- Publication
Algebra Colloquium, 2024, Vol 31, Issue 1, p11
- ISSN
1005-3867
- Publication type
Article
- DOI
10.1142/S1005386724000038