斜对称q-分圆陪集及其应用研究

引入斜对称q2-分圆陪集及斜非对称偶的概念,深入考察了n=q2m-1时斜对称分圆陪集及斜非对称偶的性质及确定方法.以此为基础研究了Hermite对偶包含BCH码的极大设计距离.解决了前人留下的一个疑难问题,并改进了前人的一个判别上界,所得到的界是紧的.再利用所得到的满足Hermite对偶包含条件的非狭义BCH码构造出一些具有很好参数的量子纠错码,这些量子码超过已有文献中由狭义BCH码构造的量子纠错码.

A Study of Skew Symmetric q-cyclotomic Coset and Its Application

On the basis of concepts of skew symmetric-cyclotomic coset and skew asymmetric coset pair,and their properties deeply studied,and methods determined,a maximal design distance of BCH codes with length contained in its Hermitian dual is studied.Thus,such an unsolved problem for maximal design distance of BCH codes with length is solved,upper bound of maximal design distance of BCH codes previously known is improved,and a new upper bound picked up is sharp.By utilizing these Hermitian dual containing non-narr...