New binary sequences with good correlation based on high-order difference and interleaving techniques

An important and well-studied problem with many applications in communication systems is to find sequences with good correlation property that means auto- and cross-correlations of the sequences are all very small comparing with their periods. This paper focuses on sequences of period 2^r - 1(r>> 1) with infinite third depth and shows that the difference operator really works with the interleaving technique on producing sequences with good correlation property and long period N = 2^2r-2^r+1+1, which are constructed from 2-level autocorrelation sequences of period 2^r - 1 except m-sequences. The method is lightweight since the computational complexity is O(p√N) and only the XOR logical operator is used.