New sets of optimal p-ary low-correlation zone sequences

Abstract

In this correspondence, three methods of constructing lowcorrelation zone (LCZ) sequences are proposed. In the first method, we constructed binary LCZ sequence sets of period 2(n) -1 using the Legendre sequences of period 2(m) -1 as a column sequence when m vertical bar n. In the second method, we devise a column sequence set of length 2(m+1) -1 from a binary sequence of period 2(m) -1 having ideal autocorrelation property and this column sequence set is used to construct binary LCZ sequence sets of period 2(n) -1 when (m + 1) vertical bar n. In the third method, p-ary LCZ sequence sets are constructed by adopting p-ary sequence of period p(m) -1 with ideal autocorrelation for integers n and m such that m vertical bar n as a column sequence. The second and third methods give us the optimal sets with respect to the bound by Tang, Fan, and Matsufuji. Finally, a construction method of p(n) x p(n) p-ary Hadamard matrices from optimal LCZ sequence sets is proposed.