Compression of Periodic Complementary Sequences and Applications
Abstract
A collection of complex sequences of length v is complementary if the sum of their periodic autocorrelation function values at all non-zero shifts is constant. For a complex sequence A=[a0,a1,...,av-1] of length v=dm we define the m-compressed sequence A(d) of length d whose terms are the sums ai + ai+d + ... + ai+(m-1)d. We prove that the m-compression of a complementary collection of sequences is also complementary. The compression procedure can be used to simplify the construction of complementary +1,-1-sequences of composite length. In particular, we construct several supplementary difference sets (v;r,s;lambda) with v even and lambda=(r+s)-v/2, given here for the first time. There are 15 normalized parameter sets (v;r,s;lambda) with v <= 50 for which the existence question was open. We resolve all but one of these cases.