On the Construction of Nonbinary Quantum BCH Codes
Quantum Physics
2016-11-17 v2 Information Theory
math.IT
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.
Cite
@article{arxiv.1212.5687,
title = {On the Construction of Nonbinary Quantum BCH Codes},
author = {Giuliano G. La Guardia},
journal= {arXiv preprint arXiv:1212.5687},
year = {2016}
}