Hermitian dual-containing constacyclic BCH codes and related quantum codes of length $\frac{q^{2m}-1}{q+1}$

Abstract

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 (