2020/07/27 by X. Zhao, Zhao, X., X. Li +5
Computer Science · Mathematics · #94B05 #94B15 #94B50 #FOS: Computer and information sciences #H.4.3 #Information Theory (cs.IT) #acm:94B05 #acm:94B15 #acm:94B50 #cs.IT #math.IT #msc:94B05 #msc:94B15 #msc:94B50
paper · pdf · doi:10.48550/arxiv.2007.13309
16pages, 3 tables
arxiv created 2020/07/27 · arxiv updated 2020/07/28
In this paper, we study a family of constacyclic BCH codes over \mathbbFq2 of length n=\fracq2m-1q+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=\fracq2m-1q+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.).