Boolean Functions of Binary Type-II Complementary Array Pair

Erzhong Xue, Zilong Wang, Jinjin Chai

Abstract: Binary Type-II complementary pairs are shown to exist only at lengths <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$2^{m}$</tex> , and exhaustive search for binary Type-II complementary sequence pairs of small length shows that the algebraic normal form of these pairs must satisfy specified expression. However, it is still open whether this expression of algebraic normal form determines all the binary Type-II complementary sequence pairs. In this paper, we proved that sequence pairs with such expression must be Type-II complementary sequence pairs, and this expression of algebraic normal form determines all the binary Type-II complementary array pairs of size <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$2\times 2\times\cdots\times 2$</tex>