Let $\mathbb{F}_p$ be a finite field and $u$ be an indeterminate. This article studies $(1-2u^2)$-constacyclic codes over the ring $\mathbb{F}_p+u\mathbb{F}_p+u^2\mathbb{F}_p$, where $u^3=u$. We describe generator polynomials of this kind of codes and investigate the structural properties of these codes by a decomposition theorem.

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].

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 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 .

As a generalization of BCH codes, constacyclic codes have become good source for constructing optimal codes. However, the parameters these are not easy to determine in general. In this paper, we investigate class $ q $-ary with length \frac{q^{m}+1}{2} and compute their exact dimensions some ranges designed distance. particular, study distance larger range than known results.