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Erschienen in:
01.05.2021
A family of Hermitian dual-containing constacyclic codes and related quantum codes
Erschienen in: Quantum Information Processing | Ausgabe 5/2021
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Abstract
In this paper, we study a family of constacyclic BCH codes over \({\mathbb {F}}_{q^2}\) of length \(n=\frac{q^{2m}-1}{q+1}\), where q is a prime power, and \(m\ge 2\) an even integer. The maximum designed distance of narrow-sense Hermitian dual-containing constacyclic BCH codes over \({\mathbb {F}}_{q^2}\) of length n is determined. Furthermore, the exact dimensions of these constacyclic BCH codes with given designed distance are obtained. As a consequence, we are able to derive the parameters of quantum codes as a function of their designed parameters of the associated constacyclic BCH codes. This improves a recent result by Yuan et al. (Des Codes Cryptogr 85(1): 179–190, 2017) for codes with the same lengths except three trivial cases (\(q=2, 3, 4\)). Moreover, some of our newly constructed quantum codes have better parameters compared with those constructed recently (Song et al. Quantum Inf Process 17(10): 1–24, 2018, 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(10): 1–40, 2019).