New Families of Balanced Quaternary Sequences of Even Period With Three-Level Optimal Autocorrelation

Abstract

In this letter, we present two new families of balanced quaternary sequences of period N = 2p with optimal three-level autocorrelation, where p = 4f + 1 is an odd prime and has a quadratic partition of form either p = 4y <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> + 1 (y is even) or p = 4+ x <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> (x is odd). Our construction is based on the Chinese remainder theorem and cyclotomic classes of order four.