New Quantum MDS codes constructed from Constacyclic codes

TL;DR

This paper introduces new quantum MDS codes derived from constacyclic codes and Hermitian construction, expanding the set of available codes with parameters not previously documented.

Contribution

The paper presents novel quantum MDS codes constructed from constacyclic codes and Hermitian methods, with parameters not covered by existing literature.

Findings

Most codes have new parameters not previously documented

Constructed codes are of the form q=2am+t, n=(q^2+1)/a

Codes demonstrate improved or unique quantum error correction capabilities

Abstract

Quantum maximum-distance-separable (MDS) codes are an important class of quantum codes. In this paper, using constacyclic codes and Hermitain construction, we construct some new quantum MDS codes of the form $q=2am+t$, $n=\frac{q^{2}+1}{a}$. Most of these quantum MDS codes are new in the sense that their parameters are not covered be the codes available in the literature.