p元m序列与其采样序列之间的互相关性

On cross-correlation between p-ary m-sequence and its decimated sequence

设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{tr1n(αt)}与其采样序列{tr1n(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。

Let p be an odd prime and n be even positive integer with gcd（n- 1 ,p＋ 1）= 1 .For d=（p^（n-1） ＋ 1）/（p＋ 1） ,the crosscorrelation between the p-ary m-sequence {tr 1^n（a^t）} and its decimated sequence {tr 1^n（a^dt）} is investigated,where a is the primitive element of F..The possible values of the crosscorrelation function Cd（r） are determined and the probability of ｜Ca（r）＋1｜〈p^n/（2＋1） is also determined.Whenn is big enough,this probability approximates to 1.