New design of quaternary low-correlation zone sequence sets and quaternary Hadamard matrices

In this correspondence, we present new construction methods for quaternary low-correlation zone (LCZ) sequence sets from a binary sequence with good autocorrelation. We show that the sets obtained by our methods are optimal or nearly optimal with respect to the Tang-Fan-Matsufuji bound and that our construction methods are more flexible than any other previous constructions in the sense of period, family size, and zone size. We also give a construction method for a quaternary LCZ sequence set from a binary LCZ sequence set. Finally, we give a new construction method for quaternary Hadamard matrices by the inverse of the Gray map.