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New Quantum BCH Codes of Length n = r(q2 − 1)
International Journal of Theoretical Physics ( IF 1.3 ) Pub Date : 2021-01-01 , DOI: 10.1007/s10773-020-04673-0
Hao Zhang , Shixin Zhu

Classical Bose-Chaudhuri-Hocquenghem (BCH) codes over finite fields have studied extensively. The quantum stabilizer codes with good parameters can be constructed using classical BCH codes. In this paper, we study the construction of quantum codes from nonprimitive BCH codes over the finite field F q 2 $\mathbb {F}_{q^{2}}$ . Taking advantage of Hermitian dual containing BCH codes of length n = r ( q 2 − 1) over F q 2 $\mathbb {F}_{q^{2}}$ where ord n ( q 2 ) = 4, we can construct some families of new quantum codes with good parameters.

中文翻译:

长度为 n = r(q2 − 1) 的新量子 BCH 码

有限域上的经典 Bose-Chaudhuri-Hocquenghem (BCH) 码已得到广泛研究。可以使用经典的 BCH 代码构建具有良好参数的量子稳定器代码。在本文中,我们研究了在有限域 F q 2 $\mathbb {F}_{q^{2}}$ 上从非原始 BCH 码构造量子码。利用包含长度为 n = r ( q 2 − 1) 的 Hermitian 对偶 BCH 码而不是 F q 2 $\mathbb {F}_{q^{2}}$ 其中 ord n ( q 2 ) = 4,我们可以构造一些具有良好参数的新量子代码族。
更新日期:2021-01-01
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