A Direct Construction of GCP and Binary CCC of Length Non Power of Two

TL;DR

This paper introduces a novel direct method to construct Golay complementary pairs and binary complete complementary codes of non-power of two lengths, expanding their applicability in communication systems.

Contribution

It presents a new construction technique using generalized Boolean functions to generate GCPs, MOCSs, and binary CCCs of arbitrary non-power of two lengths.

Findings

Constructed GCPs of non-power of two lengths using GBF truncation.

Generated MOCSs with specific non-power of two lengths.

Binary CCCs achieved with column sequence PMEPR effectively bounded by 2.

Abstract

Golay complementary pairs (GCPs) and complete complementary codes (CCCs) have found a wide range of practical applications in coding, signal processing and wireless communication due to their ideal correlation properties. In fact, binary CCCs have special advantages in spread spectrum communication due to their simple modulo-2 arithmetic operation, modulation and correlation simplicity, but they are limited in length. In this paper, we present a direct construction of GCPs, mutually orthogonal complementary sets (MOCSs) and binary CCCs of non-power of two lengths to widen their application in the recent field. First, a generalised Boolean function (GBF) based truncation technique has been used to construct GCPs of non-power of two lengths. Then Complementary sets (CSs) and MOCSs of lengths of the form $2^{m-1}+2^{m-3}$ ($m \geq 5$) and $2^{m-1}+2^{m-2}+2^{m-4}$ ($m \geq 6$) are generated by GBFs. Finally, binary CCCs with desired lengths are constructed using the union of MOCSs. The row and column sequence peak to mean envelope power ratio (PMEPR) has been investigated and compared with existing work. The column sequence PMEPR of resultant CCCs can be effectively upper bounded by $2$.