Let m, e be positive integers, p a prime number, Fpm be a finite field of p elements and R = Fpm [u]/〈u 〉 which is a finite chain ring. For any ω ∈ R and positive integers k, n satisfying gcd(p, n) = 1, we prove that any (1+ωu)-constacyclic code of length pn over R is monomially equivalent to a matrix-product code of a nested sequence of p cyclic codes with length n over R and a p × p matrix Ap...

The hulls of linear and cyclic codes have been extensively studied due to their wide applications. The dimensions and average dimension of the Euclidean hull of linear and cyclic codes have been well-studied. In this paper, the average dimension of the Hermitian hull of constacyclic codes of length n over a finite field Fq2 is determined together with some upper and lower bounds. It turns out t...

We study (1 + 2v)-constacyclic codes over R + vR and their Gray images, where v + v = 0 and R is a finite chain ring with maximal ideal  and nilpotency index e. It is proved that the Gray map images of a (1 + 2v)-constacyclic codes of length n over R + vR are distance-invariant linear cyclic codes of length 2n over R. The generator polynomials of this kind of codes for length n are determined,...

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.

For an odd prime $ p and positive integers m \ell $, let \mathbb{F}_{p^m} be the finite field with p^{m} elements R_{\ell,m} = \mathbb{F}_{p^m}[v_1,v_2,\dots,v_{\ell}]/\langle v^{2}_{i}-1, v_{i}v_{j}-v_{j}v_{i}\rangle_{1\leq i, j\leq \ell} $. Thus is a commutative non-chain ring of order p^{2^{\ell} m} characteristic In this paper, we aim to construct quantum codes from skew constacyclic over F...

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-dua...

Skew polynomial rings over finite fields ([7] and [10]) and over Galois rings ([8]) have been used to study codes. In this paper, we extend this concept to finite chain rings. Properties of skew constacyclic codes generated by monic right divisors of x − λ, where λ is a unit element, are exhibited. When λ = 1, the generators of Euclidean and Hermitian dual codes of such codes are determined tog...