一类P元序列集的相关性和线性复杂度的分析

对于素数P和偶数n=2k，构造了一类周期为P^n-1的P”条序列组成的P元序列集s（r），这里P^k≠2（rood3），r与P^k=1互素．利用d-齐次函数的性质，确定了这类序列集的相关函数取-1±P^k-1，-1＋2·p^k四值及相应分布；使用推广的Key方法证明了这类序列集具有较大的线性复杂度下界．这类序列集可适用于CDMA通信系统和密码系统中．

On Correlation and The Linear Span of a Class of p -ary Sequences Family

For any prime number p and even n= 2k , a family of p-ary sequences S（r） containing p^n -sequences of period p^n- 1 was proposed, where pP^k≠2（rood3）,r and r relatively prime to p^n --1. Based on d-form function, it is proved that the nontriviaI crosscorrelation values are -1± pk, - 1, -1 ＋ 2 · p^k , and the correlation distribution is completely determined. The low bound of linear spans of the proposed family is proved to be large by generalized key methods. This family of sequences is suitable for CDMA systems and cryptography.