Two Families of BCH Codes and New Quantum Codes

In this paper, two families of Hermitian dual-containing Bose-Chau- dhuri-Hocquenghem (BCH) codes with length n=a⋅q2+12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$n=a\cdot \frac {q^{2}+ 1}{2}$\end{document} and n = b (q2 + 1) are studied, where odd a∣(q − 1) for odd prime power q and b∣ (q + 1) for even prime power q, respectively. Using these non-narrow-sense BCH codes, some new quantum BCH codes are constructed. Most of these quantum codes have better parameters than the ones in the literature.