k=2^(m)-1阶分圆数的计算  

The cyclotomic numbers of order k=2^(m)-1

作　　者：董军武[1] 张晓磊 余玉银 DONG Jun-wu;ZHANG Xiao-lei;YU Yu-yin(School of Mathematics and Information Science,Guangzhou University,Guangzhou 510006,China)

机构地区：[1]广州大学数学与信息科学学院,广东广州510006

出　　处：《广州大学学报（自然科学版）》2022年第3期29-36,54,共9页Journal of Guangzhou University:Natural Science Edition

基　　金：The NSF of China (61502113);the Guangdong Provincial NSF (2015A030310174)。

摘　　要：令n=2m是偶数,k=2^(m)-1,文章给出了有限域F_(2n)上所有k阶分圆数的计算公式,研究了这些分圆数的值分布规律。这些结果可用于构造一类de Bruijn序列,构造方式是对通过合并不可约线性移位寄存器的状态圈得到的,这类de Brjijn序列,合并的状态圈数是最多的。Let n=2m be an even number, for k=2^(m)-1, we provide a method to calculate all the corresponding k-th cyclotomic numbers a_(i,j) over the finite field F_(2n), and study the value distribution of the k-th cyclotomic matrix. These results can be used to construct a class of de Bruijn sequences by jointing all the cycles of the graph state of the linear shift register with irreducible connective polynomials, and the number of cycles that are joined is as many as possible.

关 键 词：分圆类 分圆数 有限域 迹 de Bruijn序列 

分 类 号：O153.4[理学—数学]