Abstract:

Let p be an odd prime and n be even positive integer with gcd(n - 1p + 1) = 1 .For d = (pn - 1 + 1)/(p + 1) ，the crosscorrelation between the p -ary m -sequence {tr n1 (αt)} and its decimated sequence {tr n1 (αdt)} is investigated，where α is the primitive element of Fpn .The possible values of the crosscorrelation function Cd (τ) are determined and the probability of|Cd (τ) + 1| £ pn/2 + 1 is also determined.When n is big enough，this probability approximates to 1 .

Key words: cross-correlation function, exponential sum, p -ary m -sequences, finite fields

摘要： p 是奇素数，n 为一正偶数，且满足gcd(n - 1p + 1) = 1 。令d = (pn - 1 + 1)/(p + 1) ，α 是有限域Fpn 的本原元，研究了周期为pn - 1 的p 元m 序列{tr n1 (αt)} 与其采样序列{tr n1 (αdt)} 之间的互相关性，确定了相关函数Cd (τ) 的所有可能取值，并得到了|Cd (τ) + 1| £ pn/2 + 1 的概率。当n 充分大时，该概率接近1 。

关键词: 相关函数, 指数和, p 元m 序列, 有限域