Pure Asymmetric Quantum MDS Codes from CSS Construction: A Complete Characterization

TL;DR

This paper constructs pure CSS asymmetric quantum MDS codes that reach the quantum Singleton bound, providing a complete characterization assuming the classical MDS Conjecture, thus advancing quantum error correction theory.

Contribution

It offers a complete characterization of pure CSS asymmetric quantum MDS codes under the classical MDS Conjecture, covering all possible parameters.

Findings

Constructed pure CSS asymmetric quantum MDS codes attaining the quantum Singleton bound.

Provided a complete parameter classification assuming the classical MDS Conjecture.

Established the existence of such codes for all feasible parameters.

Abstract

Using the Calderbank-Shor-Steane (CSS) construction, pure $q$-ary asymmetric quantum error-correcting codes attaining the quantum Singleton bound are constructed. Such codes are called pure CSS asymmetric quantum maximum distance separable (AQMDS) codes. Assuming the validity of the classical MDS Conjecture, pure CSS AQMDS codes of all possible parameters are accounted for.