| 一类不可约多项式的邻接矩阵 |
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| 引用本文： | 董军武,裴定一.一类不可约多项式的邻接矩阵[J].数学学报,2018,61(5):843-856. |
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| 作者姓名： | 董军武 裴定一 |
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| 作者单位： | 广州大学数学与信息科学学院 广州 510006 |
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| 基金项目： | 广东省自然科学基金项目（2015A030310174）；广州市属高校科技计划项目（1201420765） |
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| 摘 要： | Dong和Pei在文Construction for de Bruijn sequences with large stage,Des.Codes Cryptogr,2017,85(2):343-358]中利用F_2x]的n次不可约多项式构造大级数de Bruijn序列.不可约多项式的邻接矩阵从理论上给出了这种方法能构造de Bruijn序列的数目.我们给出一类特殊不可约多项式的邻接矩阵,从理论上给出了用这类不可约多项式能够构造的de Bruijn序列的数目.
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The Adjacency Matrix of Some Class of Irreducible Polynomials |
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| Jun Wu DONG,Ding Yi PEI.The Adjacency Matrix of Some Class of Irreducible Polynomials[J].Acta Mathematica Sinica,2018,61(5):843-856. |
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| Authors: | Jun Wu DONG Ding Yi PEI |
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| Institution: | College of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, P. R. China |
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| Abstract: | InConstruction for de Bruijn sequences with large stage, Des. Codes Cryptogr, 2017, 85(2):343-358], the authors constructed many de Bruijn sequences with large stages, by using irreducible polynomials with degree n. From the adjacency matrix of the irreducible polynomial, one can calculate the number of de Bruijn sequences in theory that can be constructed by the methods in6]. We calculate the adjacency matrix of a special class of irreducible polynomials, which has degree n and periods l=(2n -1)/3 and l=(2n -1)/5. |
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| Keywords: | de Bruijn sequence irreducible polynomial adjacency matrix cyclotomic coset |
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