Synthesis of four-level Z-complementary sequences

Sequences over the alphabet {1, -1, 2, -2} are called four-level sequences. Including the conventional complementary sets as special cases, the aperiodic four-level Z-complementary sets (FLZCS) with zero correlation zone (denoted by Z) are introduced, and the elementary transformations on four-level sequences and elementary operations on FLZCS are given. In particular, comparing four-level Z-complementary pairs with binary and quadriphase Z-complementary ones, the results show that the maximum zero correlation zone (denoted by Z_max) of four-level and quadriphase Z-complementary pairs is generally much longer than that of binary Z-complementary ones, and that Z_max of four-level Z-complementary pairs is pretty close to that of quadriphase Z-complementary ones. It is verified that most synthesizing methods of quadriphase Z-complementary sets and their mates are also applicable to FLZCS, in addition to which, other synthesizing methods of FLZCS and their mates are provided here.