Dual Containing BCH Codes and New Asymmetric Quantum Codes

Abstract

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 = 4^m - 1 where m = 2l and mm =2l±1 , we construct two families of new asymmetric quantum codes with d_z ≥ δ_max +1, where δ_max 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.