  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=[a_0,a_1,...,a_{v-1}] of length v=dm we
define the m-compressed sequence A^{(d)} of length d whose terms are the sums
a_i + a_{i+d} + ... + a_{i+(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.
