新的具有大线性复杂度的4值低相关序列集

New family of binary sequences with 4-valued correlation and large linear span

设正整数n、m和r满足n=4m,r=2 m-1-1,基于Niho序列集和d型函数构造了一类4值低相关序列集S(r)。该序列集中序列的数目为2n,相关函数的最大边峰值2(n+2)/2+1,序列的周期为2 n-1。通过Key的方法,证明了该序列集中序列线性复杂度的下界为n(2 n/2-3+2)。该序列集与江文峰等人构造的序列集具有相同的相关函数值和序列数目,但拥有更大的线性复杂度。

Let n,m,and r be three positive integers with n=4m and r=2m？1？1.Based on Niho＇s sequences set and d-form function,a new family S（r） of binary sequences with 4-valued low correlation was proposed.This new family contains 2n sequences of period 2n？1 with maximal nontrivial correlation value 2（n＋2）/2＋1.By using key＇s method,the linear spans of the sequences family was lower bounded by n（2n/2？3＋2）.Compared with the best known sequences family constructed by Jiang Wen-feng et al,the new family has not only the same correlation values and family size,but also has much larger linear span.