Hermitian dual containing BCH codes and Construction of new quantum codes
Ruihu Li, Fei Zou, Yang Liu, Zongben Xu · Quantum Information and Computation · 2013
Let $q\geq 3$ be a prime power. Maximal designed distances of primitive Hermitian dual containing $q^{2}$-ary BCH codes (narrow-sense or non-narrow-sense) are determined by a careful analysis of properties of cyclotomic cosets. Non-narrow-sense BCH codes which achieve these maximal designed distances are presented, and a sequence of nested non-narrow-sense BCH codes that contain these BCH codes with maximal designed distances are constructed and their parameters are computed. Consequently, new nonbinary quantum BCH codes are derived from these non-narrow-sense BCH codes. The nonbinary quantum BCH codes presented here have better parameters than those quantum BCH codes available in the literature.