环Z_p^l导出Kerdock-code序列的部分周期性质  

Partial Period Properties of the Kerdock-code Sequences Derived from Z_p^l

作　　者：孙霓刚[1] 胡磊[2] 郑红[3] 

机构地区：[1]常州大学信息科学与工程学院,江苏常州213164 [2]中国科学院信息工程研究所信息安全国家重点实验室,北京100093 [3]华东理工大学计算机科学与工程系,上海200237

出　　处：《电子学报》2014年第11期2162-2167,共6页Acta Electronica Sinica

基　　金：国家自然科学基金(No.61103172;No.61103115)

摘　　要：对环Zpl导出的多元Kerdock-code序列的部分周期性质进行了研究,这里p为任意奇素数,l为任意正整数.利用特征为pl的Galois环上不完全指数和的非平凡上界,对上述p元Kerdock-code序列的非周期自相关性及互相关性进行了估计,同时对序列的部分周期分布和部分周期独立r-样式分布也进行了刻画.结果表明,此类序列具有极低的非周期自相关性及互相关性,同时其部分周期分布和部分周期独立r-样式分布也是渐进均匀的,在密码学和通信领域具有潜在的应用价值.The partial period properties of the Kerdock-code sequences derived from Zplare studied,where p is an odd prime and l is an arbitrary positive integer. Utilizing a nontrivial upper bound for the incomplete exponential sums over Galois rings of characteristic p^l,we obtain the upper bounds for the aperiodic autocorrelation and crosscorrelation of the p-ary Kerdockcode sequences derived from Zp^l. Also we analyze the partial period distributions and the partial period independent r-pattern distributions of these sequences. The results show that such sequences have low aperiodic autocorrelation and crosscorrelation,and their partial period distributions and partial period independent r-pattern distributions are asymptotically uniform,which indicates that these sequences have strong potential applications in communication systems and cryptography.

关 键 词：Kerdock-code序列 Galois环上的不完全指数和 非周期相关性 部分周期分布 r-样式 

分 类 号：TN918.1[电子电信—通信与信息系统]