1 research outputs found
Hermitian dual-containing constacyclic BCH codes and related quantum codes of length
In this paper, we study a family of constacyclic BCH codes over
of length , where is a prime
power, and an even integer. The maximum design distance of
narrow-sense Hermitian dual-containing constacyclic BCH codes of length 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 (), our resultant quantum codes can
always yield strict dimension or minimum distance gains than the ones obtained
by Yuan et al.. Moreover, fixing length , 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.).Comment: 16pages, 3 table