Dual Containing BCH Codes and New Asymmetric Quantum Codes

In this paper, we discuss the problem on the construction of asymmetric quantum codes [[n, k, dz/dx]]4 from primitive narrow sense BCH codes. Take advantage of dual containing BCH codes of length n = 4m -- 1 where m = 2l and m = 2l + 1, we construct two families of new asymmetric quantum codes with dz ≥ δmax + 1, where δmax is the maximal designed distance of dual containing narrow sense BCH code. Our asymmetric quantum codes are new ones, and are not included in the known literature.