New quantum MDS codes derived from constacyclic codes

TL;DR

This paper introduces new quantum MDS codes derived from classical constacyclic codes, achieving parameters that surpass existing codes in the literature, thus advancing quantum error correction capabilities.

Contribution

The paper constructs two new classes of quantum MDS codes from constacyclic codes with improved parameters over previous known codes.

Findings

Constructed quantum MDS codes with parameters [[λ(q-1), λ(q-1)-2d+2, d]]_q.

Codes have larger minimum distances than existing codes.

Parameters depend on the divisibility of q+1 by λ, with different bounds for r even or odd.

Abstract

Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. It is very hard to construct quantum MDS codes with relatively large minimum distance. In this paper, based on classical constacyclic codes, we construct two classes of quantum MDS codes with parameters $$[[\lambda(q-1),\lambda(q-1)-2d+2,d]]_q$$ where $2\leq d\leq (q+1)/2+\lambda-1$, and $q+1=\lambda r$ with $r$ even, and $$[[\lambda(q-1),\lambda(q-1)-2d+2,d]]_q$$ where $2\leq d\leq (q+1)/2+\lambda/2-1$, and $q+1=\lambda r$ with $r$ odd. The quantum MDS codes exhibited here have parameters better than the ones available in the literature.