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Hermitian dual-containing constacyclic BCH codes and related quantum codes of length q^2m-1/q+1

by   X. Zhao, et al.
Carleton University
china university of petroleum
NetEase, Inc

In this paper, we study a family of constacyclic BCH codes over 𝔽_q^2 of length n=q^2m-1/q+1, where q is a prime power, and m≥2 an even integer. The maximum design distance of narrow-sense Hermitian dual-containing constacyclic BCH codes of length n is determined. Furthermore, the exact dimension of the constacyclic BCH codes with given design distance is computed. As a consequence, we are able to derive the parameters of quantum codes as a function of their design parameters of the associated constacyclic BCH codes. This improves the result by Yuan et al. (Des Codes Cryptogr 85(1): 179-190, 2017), showing that with the same lengths, except for three trivial cases (q=2,3,4), our resultant quantum codes can always yield strict dimension or minimum distance gains than the ones obtained by Yuan et al.. Moreover, fixing length n=q^2m-1/q+1, some constructed quantum codes have better parameters or are beneficial complements compared with some known results (Aly et al., IEEE Trans Inf Theory 53(3): 1183-1188, 2007, Li et al., Quantum Inf Process 18(5): 127, 2019, Wang et al., Quantum Inf Process 18(8): 323, 2019, Song et al., Quantum Inf Process 17(10): 1-24, 2018.).


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