ON CROSS-CORRELATION OF A BINARY m-SEQUENCE OF PERIOD 2(2k)-1 AND ITS DECIMATED SEQUENCES BY (2(lk)+1)/(2(l)+1)

摘要

For two odd integers 1, k with 0 < 1 < k and gcd(l, k) = 1, let m = 2k and d = 2(lk)+1/2(l)+1 In this paper, we study the cross-correlation between a binary m-sequence (s(t)) of length 2(m) - 1 and its d-decimated sequences (s(dt+u)), 0 <= u < 2(k) + 1/3. It is shown that the maximum magnitude of cross -correlation values is 2(m/2+1) + 1. Moreover, a new sequence family with maximum correlation magnitude 2(m/2+1) + 1 and family size 2(m/2) is proposed.