A family of negacyclic BCH codes of length $n=\frac {q^{2m}-1}{2}$
A family of negacyclic BCH codes of length $n=\frac {q^{2m}-1}{2}$
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DOI：
10.1007/s12095-019-00387-1
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发表时间：
2020-03
期刊：
影响因子：
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通讯作者：
Guanmin Guo;Ruihu Li;Yang Liu;Junli Wang
中科院分区：
文献类型：
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作者：
Guanmin Guo;Ruihu Li;Yang Liu;Junli Wang
本文研究了一类具有长度的q ~ 2元窄意义和非窄意义双循环BCH码，其中q为奇素数方幂，m ≥ 3为奇数.提出了狭义和非狭义双循环BCH码的Hermitian对偶包含条件，并精确计算了这些双循环BCH码的最大设计距离所能达到的维数.因此，许多新的q元量子码可以从这些对偶包含的双循环BCH码中导出。此外，这些新的量子码的参数优于或等于文献中提供的参数，并且比经典BCH码具有更大的设计距离。
In this paper, we investigate a family ofq2-ary narrow-sense and non-narrow-sense negacyclic BCH codes with length, whereqis an odd prime power andm≥ 3 is odd. We propose Hermitian dual-containing conditions for narrow-sense and non-narrow-sense negacyclic BCH codes, and precisely compute the dimensions of these negacyclic BCH codes whose maximal designed distance can achieve. Consequently, many newq-ary quantum codes can be derived from these dual-containing negacyclic BCH codes. Moreover, these new quantum codes are presented either with parameters better than or equal to the ones available in the literature, and also have larger designed distance than those from classical BCH codes.