一类周期为偶数的二元序列的自相关值

Autocorrelation values of a binary sequences with even length

设N为奇数,Z_N为模N的剩余类环。本文得到的主要结果有:(1)若D为Z_N上(N,(N-1)/2,(N-3)/4)的差集,=Z_N\D,{si}为以C_1=({0}×D)∪{1}×()为特征集的长度为2N的二元序列,则此序列的自相关值为4值,去掉两个特殊点,该序列最优。(2)若D为Z_N上(N,(N-1)/2,(N-5)/4,(N-1)/2)的几乎差集,=Z_N\D,{si}为以C_1=({0}×D)∪{1}×)为特征集的长度为2N的二元序列,则此序列的自相关值为6值。最后,本文还给出了长度为4N的周期序列的自相关值。

Let N be the odd number and Z N be the residual class ring of modular N,the paper obtains the main results as follows:(1)If D is a N,N-1 2,N-3 4 difference set over Z N,=Z N\D,the binary sequence{s i}of length 2N with a characteristic set C 1={0}×D∪{1}×,then its autocorrelation value is four-valued.If two special points are removed,the sequence is optimal.(2)If D is a N,N-1 2,N-5 4,N-1 2 almost difference set over Z N,=Z N\D,the binary sequence{s i}of length 2N with a characteristic set C 1={0}×D∪{1}×,then its autocorrelation value is six-valued.Finally,this paper also gives the autocorrelation values of a sequence of periodic 4N.