Some Hermitian Dual Containing BCH Codes and New Quantum Codes

Abstract

Let q= 3l+ 2 be a prime power. Maximal designed distances of imprimitive Hermitian dual containing q 2 -ary narrow-sense (NS) BCH codes of length n = (q 6−1) 3 and n = 3(q 2 − 1)(q 2 + q+ 1) are determined. For each given n, non-narrow-sense (NNS) BCH codes which achieve such maximal designed distances are presented, and a series of NS and NNS BCH codes are constructed and their parameters are computed. Consequently, many families of q-ary quantum BCH codes are derived from these BCH codes. Some of these quantum BCH codes constructed from NNS BCH codes have better parameters than those quantum BCH codes available in the literature, and some others are new ones.