Existence of Binary $Z$-Complementary Pairs

Abstract

The conventional binary complementary pairs exist only for very limited lengths, while binary <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</i> -complementary pairs exist for many more lengths. In this letter, an upper bound on zero correlation zone (ZCZ) width of binary <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</i> -complementary pairs of odd length is established. The existence conjecture of binary <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</i> -complementary pairs with ZCZ widths 2, 3, 4, 5 and 6 is completely solved, and a new recursive construction of binary <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</i> -complementary pairs is proposed.