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

Abstract

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 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> -1 using the Legendre sequences of period 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> -1 as a column sequence when m|n. In the second method, we devise a column sequence set of length 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m+1</sup> -1 from a binary sequence of period 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> -1 having ideal autocorrelation property and this column sequence set is used to construct binary LCZ sequence sets of period 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> -1 when (m+1)|n. In the third method, p-ary LCZ sequence sets are constructed by adopting p-ary sequence of period p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> -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 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> timesp <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> p-ary Hadamard matrices from optimal LCZ sequence sets is proposed