New quantum mds constacyl{\i}c codes

TL;DR

This paper introduces four new families of quantum MDS codes derived from constacyclic codes over finite fields, expanding the known constructions and generalizing previous results in quantum coding theory.

Contribution

The paper presents novel constructions of quantum MDS codes using constacyclic codes, including a generalization of existing theorems and four new code families.

Findings

Four new quantum MDS code families constructed

Extension of previous theorems in quantum code construction

Explicit generalization of prior quantum code constructions

Abstract

This paper is devoted to the study of the construction of new quantum MDS codes. Based on constacyclic codes over Fq2 , 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].