论文标题
Hermitian双重符合constacyclic BCH代码和相关长度的量子代码$ \ frac {q^{2m} -1} {q+1} $
Hermitian dual-containing constacyclic BCH codes and related quantum codes of length $\frac{q^{2m}-1}{q+1}$
论文作者
论文摘要
在本文中，我们研究了$ \ mathbb {f} _ {q^2} $长度$ n = \ frac {q^{2m} -1} {q+1} $的constacyclic bch代码家族，其中$ q $ $ q $是prime priend power，$ m \ geq2 $ and integer。确定了狭窄的Hermitian双重固定constacyclic BCH代码$ n $的最大设计距离。此外，计算具有给定设计距离的Constacyclic BCH代码的确切维度。结果，我们能够根据其相关的constacyclic BCH代码的设计参数得出量子代码的参数。这改善了Yuan等人的结果。 （DES代码代码Cryptogr 85（1）：179-190，2017），表明，除了三种微不足道的情况（$ q = 2,3,4 $）外，我们所得的量子代码始终可以产生严格的尺寸或最低距离的距离，比Yuan等人获得的距离，YUAN等人获得的量度的增长。 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.).
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 $m\geq2$ 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 $n=\frac{q^{2m}-1}{q+1}$, 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.).
