On the Construction of Nonbinary Quantum BCH Codes

Four quantum code constructions generating several new families of good nonbinary quantum nonprimitive nonnarrow-sense, Bose–Chaudhuri–Hocquenghem codes, are presented in this paper. The first two are based on Calderbank–Shor–Steane (CSS) construction derived from two nonprimitive Bose–Chaudhuri–Hocquenghem codes. The third one is based on Steane's enlargement of nonbinary CSS codes applied to suitable subfamilies of nonprimitive nonnarrow-sense Bose–Chaudhuri–Hocquenghem codes. The fourth construction is derived from suitable subfamilies of Hermitian dual-containing nonprimitive nonnarrow-sense Bose–Chaudhuri–Hocquenghem codes. These constructions generate new families of quantum codes whose parameters are better than the ones available in the literature.