周期为p^2的q元序列的k–错线性复杂度  

k-error linear complexity of q-ary sequence of period p^2

作　　者：吴晨煌 许春香[1] 杜小妮[3] WU Chenhuang;XU Chunxiang;DU Xiaoni(School of Computer Science and Engineering,University of Electronic Science and Technology of China,Chengdu 611731,China;Provincial Key Laboratory of Applied Mathematics,Putian University,Putian 351100,China;College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]电子科技大学计算机科学与工程学院,四川成都611731 [2]莆田学院应用数学福建省高校重点实验室,福建莆田351100 [3]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《通信学报》2019年第12期21-28,共8页Journal on Communications

基　　金：国家自然科学基金资助项目(No.61772292,No.61772022,No.61872060);国家自然科学基金国际(地区)合作交流项目NSFC-RFBR(No.61911530130);福建省自然科学基金资助项目(No.2018J01425)~~

摘　　要：基于矩阵中元素统计的方法,给出了计算周期为p2的q元序列k错线性复杂度的新方法,其中,p,q为奇素数且q为模p2的本原元。给出了一个一般性的结论及其证明,并通过列举2类周期为p2的q元序列及其实例来验证结论的正确性。该方法不需要迭代计算,通过程序实现并与现有算法进行效率比较,结果表明所给出的新算法在计算周期为p2的q元序列的k错线性复杂度方面效率明显更高。Based on element statistics in a matrix,a new efficient computing method for computing the k-error linear complexity of q-ary sequence of period p 2 was proposed,where p,q were odd primes and q modulo p2 was primitive.A general result and a concrete proof were showed.To verify the correctness of the result,two kinds of q-ary sequence of period p 2 were illustrated.Because the new method does not need iterative calculation and when it is implemented by program and compared with existing algorithms,the results show that the proposed new algorithm is significantly more efficient in calculating k-error linear complexity of q-ary sequence of period p2.

关 键 词：序列密码 q元序列 K错线性复杂度 费马商序列 广义割圆序列 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]