On a class of $(\delta+\alpha u^2)$-constacyclic codes over $\mathbb{F}_{q}[u]/\langle u^4\rangle$
نویسندگان
چکیده
Let Fq be a finite field of cardinality q, R = Fq[u]/〈u 〉 = Fq+uFq+u 2 Fq+u 3 Fq (u = 0) which is a finite chain ring, and n be a positive integer satisfying gcd(q, n) = 1. For any δ, α ∈ F×q , an explicit representation for all distinct (δ + αu)-constacyclic codes over R of length n is given, and the dual code for each of these codes is determined. For the case of q = 2 and δ = 1, all self-dual (1 + αu)-constacyclic codes over R of odd length n are provided.
منابع مشابه
Complete classification of $(\delta+\alpha u^2)$-constacyclic codes over $\mathbb{F}_{2^m}[u]/\langle u^4\rangle$ of oddly even length
Let F2m be a finite field of cardinality 2 , R = F2m [u]/〈u 〉) and n is an odd positive integer. For any δ, α ∈ F2m , ideals of the ring R[x]/〈x 2n − (δ+αu)〉 are identified as (δ + αu)-constacyclic codes of length 2n over R. In this paper, an explicit representation and enumeration for all distinct (δ + αu)constacyclic codes of length 2n over R are presented.
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