This paper is devoted to the study of the construction of new quantum MDS codes. Based on constacyclic codes over F q2 , we derive four new families of quantum MDS codes, one of which is an explicit generalization of the construction given in Theorem 7 in [22]. We also extend the result of Theorem 3.3 given in [17].

Let $\mathbb{F}_p$ be a finite field and $u$ be an indeterminate. This article studies $(1-2u^k)$-constacyclic codes over the ring $\mathcal{R}=\mathbb{F}_p+u\mathbb{F}_p+u^2\mathbb{F}_p+u^{3}\mathbb{F}_{p}+\cdots+u^{k}\mathbb{F}_{p}$ where $u^{k+1}=u$. We illustrate the generator polynomials and investigate the structural properties of these codes via decomposition theorem.

The class of constacyclic codes plays an important role in the theory or error-correcting codes. They are considered as a remarkable generalization cyclic In this paper, we study over finite Krasner hyperfields which characterize them by their generating polynomial. Moreover, dual these finding parity check

In this paper we give the structure of constacyclic codes over formal power series and chain rings. We also present necessary and sufficient conditions on the existence of MDS codes over principal ideal rings. These results allow for the construction of infinite families of MDS self-dual codes over finite chain rings, formal power series and principal ideal rings.

Let R be a finite commutative chain ring, D 2 n the dihedral group of size and [ ] ring. In this paper, we completely characterize left ideals (called -codes) when gcd ( c h r ) , = 1 . way, explore structure some skew-cyclic codes length over also × S where is an isomorphic copy As particular result, give cyclic case F p m Galois field, classification for N -codes any positive integer both cas...

In this paper, we study skew cyclic codes over the ring R = Fq + uFq + vFq + uvFq, where u 2 = u, v2 = v, uv = vu, q = p and p is an odd prime. We investigate the structural properties of skew cyclic codes over R through a decomposition theorem. Furthermore, we give a formula for the number of skew cyclic codes of length n over R.

Let R be a commutative finite chain ring of invariants (q ,s ), and Γ(R) the Teichmüller’s set of R. In this paper, the trace representation cyclic R -linear codes of length l, is presented, when gcd(l,q ) = 1. Wewill show that the contractions of some cyclic R -linear codes of length ul are γ -constacyclic R -linear codes of length l, where γ ∈ Γ(R)\{0R} and themultiplicative order of γ is u .

In previous works we considered codes defined as ideals of quotients of non commutative polynomial rings, so called Ore rings of automorphism type. In this paper we consider codes defined as modules over non commutative polynomial rings, removing therefore some of the constraints on the length of the codes defined as ideals. The notion of BCH codes can be extended to this new approach and the c...