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A collection of complex sequences of length v is complementary if the sum oftheir periodic autocorrelation function values at all non-zero shifts isconstant. For a complex sequence A=[a_0,a_1,...,a_{v-1}] of length v=dm wedefine the m-compressed sequence A^{(d)} of length d whose terms are the sumsa_i + a_{i+d} + ... + a_{i+(m-1)d}. We prove that the m-compression of acomplementary collection of sequences is also complementary. The compressionprocedure can be used to simplify the construction of complementary{+1,-1}-sequences of composite length. In particular, we construct severalsupplementary 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. Weresolve all but one of these cases.

Compression of Periodic Complementary Sequences and Applications