环 Zpl导出 Kerdock-code 序列的部分周期性质

摘要

The partial period properties of the Kerdock-code sequences derived from Zpl are 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 pl ,we obtain the upper bounds for the aperiodic autocorrelation and crosscorrelation of the p-ary Kerdock-code se-quences derived from Zpl .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 se-quences have strong potential applications in communication systems and cryptography .%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。