基于奇数阶分圆类的差集偶构造方法研究  

Research on construction methods of difference set pairs based on cyclotomic classes of odd orders

作　　者：宋晓飞[1] 申利民[1] 贾彦国 赵萌 彭秀平[1] 

机构地区：[1]燕山大学信息科学与工程学院,河北秦皇岛066004

出　　处：《燕山大学学报》2017年第6期528-533,共6页Journal of Yanshan University

基　　金：国家自然科学基金资助项目(61501395;61601401);河北省自然科学基金资助项目(F2016203293)

摘　　要：差集偶是一种直接构造二值自相关二进序列偶的数学工具,避免了间接构造法中所采用的基序列的特性影响,因而差集偶被广泛应用于密码学和编码理论。以往差集偶的构造方法主要集中在特征多项式、乘子定理和乘子猜想、偶数阶分圆类上,然而鲜有学者对奇数阶分圆类构造差集偶的方法进行研究。本文利用奇数阶分圆类的方法构造出了4类新的未知差集偶,并从分圆数的角度给出相应的证明,为差集偶的构造提供了新的途径,并扩大了已知差集偶实例的数量。Difference set pair is a kind of mathematical tool for the direct constructions of two-level correlation binary sequence pairs,and the characteristic influence of the basic sequences in indirect constructions can be avoided. So difference set pair is widely used in cryptography and encoding theory. In the past,the construction methods of difference set pairs were mainly focused on characteristic polynomials,multiplier theorem and multiplier conjecture,and cyclotomic classes of even orders. However,the methods of constructing difference set pairs based on cyclotomic classes of odd orders were studied by few scholars. In this paper,four new classes of unknown difference set pairs are constructed by using cyclotomic classes of odd orders,and the corresponding proofs are given by cyclotomic numbers. A new approach for the construction of difference set pairs is provided,and the number of instances of difference set pairs will be expanded.

关 键 词：差集偶 分圆类 分圆数 二进序列偶 

分 类 号：TN911.22[电子电信—通信与信息系统]