m序列与其Niho采样序列的互相关性研究

On Correlation Distribution between an m-sequence and Its Niho Decimation Sequences

采样因子d=2^(s)/2^(s)+12^(m)-1+1表示定义在有限域F_(2)^(n)上的Niho指数,其中n=2m,s和m均为正数且满足s<m,e_(2)(s)>e_(2)(m),s为偶数。若m为奇数,则gcd s,m=1,这种情况下互相关函数的取值分布情况已经得到确定;若m为偶数,则gcd s,m=r>1,本文将研究这种情况下周期为2^(2m)-1的m序列{s(t)}与其每一条周期为2^(2m)-1/2^(r)+1的短周期采样序列{s(dt+l)}的互相关函数的分布情况.

Let d=2^(s)/2^(s)+12^(m)-1+1be the Niho decimation over finite field F_(2)^(n),where n=2m,s and m are positive integer which satisfy s<m and e 2 s>e 2(m),s is even.If m is odd,then gcd s,m=1,the cross-correlation distribution has been determined in this situation;If m is even,then gcd s,m=r>1,we make a research on the cross-correlation function between m-sequence{s(t)}of period 2^(2m)-1 and its every d-decimation sequence{s(dt+l)}with short period 2^(2m)-1/2^(r)+1.