An equivalence relation called isometry is introduced to classify constacyclic codes over a finite field; the polynomial generators of constacyclic codes of length lp are characterized, where p is the characteristic of the finite field and l is a prime different from p.

Abstract We study the structure of constacyclic codes of length ps over the ring Fpk + uFpk + · · · + um−1Fpk in terms of ideals in the quotient ring (Fpk + uFpk + · · · + um−1Fpk)[x]/〈xp s − λ〉, where λ is a unit element in Fpk + uFpk + · · · + um−1Fpk . In particular, we complete a structural classification of constacyclic codes of length ps over Fpk + uFpk and determine their minimum Hamming...

Let q be a prime power and Fq be a finite field. In this paper, we study constacyclic codes over the ring Fq + uFq + vFq + uvFq, where u 2 = u, v2 = v and uv = vu. We characterize the generator polynomials of constacyclic codes and their duals using some decomposition of this ring. Finally we study the images of self-dual cyclic codes over F2m + uF2m + vF2m + uvF2m through a linear Gray map.

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.