Sequences with good correlation property using Gray mapping

This paper provides two construction methods of sequence using the Gray mapping. In the first method, a quaternary sequence with R_max = 2 for N ≡ 2 (mod 4) which is the same as the best known R_max, is proposed. The sequence is constructed by the Gray mapping of a binary sequence with even period and its half-period shift. The resulting quaternary sequence has the same autocorrelation distribution with that of the employed binary sequence. From binary sequences with optimal autocorrelation for even period such as Sidel´nikov sequences, Ding-Helleseth-Martinsen (DHM) sequences, and sequences from the images of polynomials, etc., we can construct quaternary sequences with R_max = 2 for period N ≡ 2 (mod 4) and R_max = 4 for period N ≡ 4 (mod 4). In constrast to the previous quaternary sequences separately designed, new quaternary sequences are constructed from many existing binary sequences with optimal autocorrelation. In the second construction, optimal quaternary LCZ sequence sets are derived from binary LCZ sequence sets which are not necessarily optimal. To the best of our knowledge, it is the first result to obtain an optimal LCZ sequence set from a non-optimal LCZ sequence set, while there are constructions to obtain LCZ sequence sets from another LCZ sequence set. Moreover, since the parameters of new quaternary LCZ sequence set in the second method are determined by the parameters of the binary LCZ sequence set, it is possible to obtain flexible quaternary LCZ sequence sets by using flexible binary LCZ sequence sets.