A direct construction of even length ZCPs with large ZCZ ratio

Abstract

This paper presents a direct construction of aperiodic q-ary (q is a positive even integer) even length Z-complementary pairs (ZCPs) with large zero-correlation zone (ZCZ) width using generalised Boolean functions (GBFs). The applicability of ZCPs increases with the increasing value of ZCZ width, which plays a significant role in reducing interference in a communication system with asynchronous surroundings. For q = 2, the proposed ZCPs reduce to even length binary ZCPs (EB-ZCPs). However, to the best of the authors’ knowledge, the highest ZCZ ratio for even length ZCPs which are directly constructed to date using GBFs is 3/4. In the proposed construction, we provide even length ZCPs with ZCZ ratios 5/6 and 6/7, which are the largest ZCZ ratios achieved to date through direct construction.