Recently, codes over some special finite rings especially chain rings have been studied. More recently, codes over finite non-chain rings have been also considered. Study on codes over such rings or rings in general is motivated by the existence of some special maps called Gray maps whose images give codes over fields. Quantum error-correcting (QEC) codes play a crucial role in protecting quantum ...

Recently, entanglement-assisted quantum error correcting codes (EAQECCs) have been constructed by cyclic codes and negacyclic codes. In this paper, by analyzing the cyclotomic cosets in the defining set of constacyclic codes, we constructed three classes of new EAQECCs which satisfy the entanglement-assisted quantum Singleton bound. Besides, three classes of EAQECCs with maximal entanglement fr...

(1+pw)-constacyclic codes of arbitrary length over the nonprincipal ideal ring Zps + uZps are studied, where p is a prime, w ∈ Z × ps and s an integer satisfying s ≥ 2. First, the structure of any (1 + pw)constacyclic code over Zps +uZps are presented. Then enumerations for the number of all codes and the number of codewords in each code, and the structure of dual codes for these codes are give...

for a finite field $mathbb{f}_q$, the bivariate skew polynomial ring $mathbb{f}_q[x,y;rho,theta]$ has been used to study codes cite{xh}. in this paper, we give some characterizations of the ring $r[x,y;rho,theta]$, where $r$ is a commutative ring. we investigate 2-d skew $(lambda_1,lambda_2)$-constacyclic codes in the ring $r[x,y;rho,theta]/langle x^l-lambda_1,y^s-lambda_2rangle_{mathit{l}}.$ a...

The results of J. F. Qian et al. [5] on (1 − γ)-constacyclic codes over finite chain rings of nilpotency index 2 are extended to (1 − γe)constacyclic codes over finite chain rings of arbitrary nilpotency index e+1. The Gray map is introduced for this type of rings. We prove that the Gray image of a linear (1− γe)-constacyclic code over a finite chain ring is a distance-invariant quasi-cyclic co...

For units δ and α in Fpm, the structure of (δ + αu 2)-constacyclic codes of length p over Fpm + uFpm + u 2 Fpm is studied and self-dual (δ + αu 2)constacyclic codes are analyzed.

Let p be an odd prime, s,m be positive integers and Fpm be the finite field with p m elements. In this paper, we determine all constacyclic codes of length 4p over the finite commutative chain ring R = Fpm + uFpm with unity, where u 2 = 0. We also determine their dual codes and list some isodual constacyclic codes of length 4p over R.

In [4], starting from an automorphism θ of a finite field Fq and a skew polynomial ring R = Fq[X; θ], module θ-codes are defined as left R-submodules of R/Rf where f ∈ R. In [4] it is conjectured that an Euclidean self-dual module θ-code is a θ-constacyclic code and a proof is given in the special case when the order of θ divides the length of the code. In this paper we prove that this conjectu...

We give the structure of λ-constacyclic codes of length pm over R = Fpr +uFpr + . . .+uFpr with λ ∈ F ∗ pr . We also give the structure of λ-constacyclic codes of length pm with λ = α1 + uα2 + . . .+ u αe−1, where α1, α2 6= 0 and study the self-duality of these codes.