On the Construction of Nonbinary Quantum BCH Codes

TL;DR

This paper introduces four novel quantum code constructions based on nonbinary BCH codes, resulting in new families of quantum BCH codes with improved parameters over existing ones.

Contribution

It presents four new methods for constructing nonbinary quantum BCH codes, expanding the available code families with better parameters.

Findings

Generated new families of quantum BCH codes with improved parameters

Utilized CSS and Steane's enlargement techniques for code construction

Achieved codes that outperform existing literature in parameters

Abstract

Four quantum code constructions generating several new families of good nonbinary quantum nonprimitive non-narrow-sense Bose-Chaudhuri-Hocquenghem (BCH) codes are presented in this paper. The first two ones are based on Calderbank-Shor-Steane (CSS) construction derived from two nonprimitive BCH codes, not necessarily self-orthogonal. The third one is based on nonbinary Steane's enlargement of CSS codes applied to suitable sub-families of nonprimitive non-narrow-sense BCH codes. The fourth construction is derived from suitable sub-families of Hermitian self-orthogonal nonprimitive non-narrow-sense BCH codes. These constructions generate new families of quantum BCH codes whose parameters are better than the ones available in the literature.