A Construction of Quaternary Low Correlation Zone Sequence Sets from Binary Low Correlation Zone Sequence Sets Improving Optimality

A New Method for Constructing Quaternary Sequence Sets with Low Correlation Zone

“…Most of the known methods use inverse mapping to map two binary variables to a quaternary one in the construction of quaternary LCZ sequence sets [6,8,9]. However, the proposed construction generates sequence set using three different mappings and the resultant sequence sets are all LCZ sequence sets.…”

“…Condition (1) and (2) (1) L odd. Let [3] (2 n − 1, 2 e − 1, (2 n − 1)/(2 e − 1), 1) 1 N o Construction in [6] (N, 2L, min(d, d h ), |δ|) 1 N o Construction in [8] (Ld + r, L, d, |δ|) or (2Ld, L, d, |δ|) 1 Y e s Construction in [9] (Ld + r, L, d, 1) k (k ≥ 1) Yes Construction in this paper (Ld + r, L, d, |δ|) n = 3k Yes or (2Ld, L, d, |δ|) n (n ≥ 1) Yes…”

“…Recently, Jang [5] presented an extension method to construct quaternary LCZ sequence set with parameters (2N, 2M, L, 2) based on quaternary LCZ sequence set with parameters (N, M, L, 1). Whereafter, Jang [6] constructed optimal quaternary LCZ sequence set using inverse Gray mapping from optimal or suboptimal binary LCZ sequence sets. However, in most of the existing constructions, the parameters of the sequence sets cannot be flexibly chosen [1,3,5,6,7].…”

“…Whereafter, Jang [6] constructed optimal quaternary LCZ sequence set using inverse Gray mapping from optimal or suboptimal binary LCZ sequence sets. However, in most of the existing constructions, the parameters of the sequence sets cannot be flexibly chosen [1,3,5,6,7]. Moreover, the number of the sequence set is restrict to one [1,2,3,5,6].…”

“…However, in most of the existing constructions, the parameters of the sequence sets cannot be flexibly chosen [1,3,5,6,7]. Moreover, the number of the sequence set is restrict to one [1,2,3,5,6]. Based on inverse Gray mapping and the binary sequence with good autocorrelation, Chung [8] constructed single quaternary LCZ sequence set with flexible choice of parameters.…”