New Sets of Optimal $p$-ary Low-Correlation Zone Sequences

In this correspondence, three methods of constructing low-correlation 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|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)|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|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
timesp
ⁿ
p-ary Hadamard matrices from optimal LCZ sequence sets is proposed