Construction of Z-Complementary Code Sets With Non-Power-of-Two Lengths Based on Generalized Boolean Functions

Abstract

$Z$ -complementary code set (ZCCS) plays a major role in modern communication systems. It has applications in multi-carrier code-division multiple access (MC-CDMA) scheme, channel estimation in multiple-input and multiple-output (MIMO) systems, etc. In this letter, we propose a construction of $q$ -ary ZCCS of a length of the form $2^{m}+2$ using generalized Boolean functions (GBFs). The constructed ZCCS is optimal with respect to the theoretical upper bound. Based on the authors’ knowledge, all the existing constructions of ZCCSs based on GBFs are limited to the lengths of power-of-two only.