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

作　　者：熊臻 岳勤[1] XIONG Zhen;YUE Qin(College of Science,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,China)

机构地区：[1]南京航空航天大学理学院,江苏南京211106

出　　处：《计算机工程与科学》2018年第9期1572-1578,共7页Computer Engineering & Science

基　　金：国家自然科学基金(61772015)

摘　　要：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.

关 键 词：差集 几乎差集 自相关函数 

分 类 号：TN918.1[电子电信—通信与信息系统]