文献类型：期刊文献

中文题名：环Z_p^l导出Kerdock-code序列的部分周期性质

英文题名：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：[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

年份：2014

卷号：42

期号：11

起止页码：2162

中文期刊名：电子学报

外文期刊名：Acta Electronica Sinica

收录：CSTPCD;;EI(收录号：20145300388090);Scopus;北大核心:【北大核心2011】；CSCD:【CSCD2013_2014】；

基金：国家自然科学基金(No.61103172;No.61103115)

语种：中文

中文关键词：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

外文关键词：Kerdock-code sequence; incomplete exponential sum over Galois rings; aperiodic correlation; partial period distribution; r-pattern

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.