Optimum complementary sets and quadriphase sequences derived from q-ary m-sequences

Sequences with perfect correlation properties (i.e., vanishing sidelobes of their autocorrelation function) are applied in navigational systems, in synchronization, and for system measurement and identification. Since only one periodic perfect binary sequence (length N=4) is known, on the one hand polyphase sequences with a larger phase alphabet, especially quadriphase sequences, and on the other hand so-called complementary sets of sequences have been applied (Golay 1961). Pairs of sequences are called aperiodic or periodic complementary sets (ACS or PCS) if the sum of their aperiodic or periodic respectively autocorrelation functions is a delta function. Complementary pairs of binary sequences cannot exist for all lengths. Therefore, sets of ternary sequences with the elements -1, 0 and 1 have been investigated. Since for technical reasons the number of zero-elements should be as small as possible, ternary complementary sets are called optimum if no set with a smaller number of zero-elements exists. Ternary aperiodic complementary sets have been investigated in Garvish and Lempel (1994). In this paper, the construction of new optimum PCS and almost perfect quadriphase sequences is described.