Group Symmetries of Complementary Code Matrices

TL;DR

This paper characterizes the symmetries of poly-phase complementary code matrices, classifies them into equivalence classes, and introduces a new construction method for generating quad-phase CCMs from ternary CCMs, with detailed classification results for small dimensions.

Contribution

It provides a comprehensive classification of CCMs based on group symmetries and introduces a novel construction method linking ternary and quad-phase CCMs.

Findings

Classification of CCMs for N=2 to 6

New construction method for quad-phase CCMs from ternary CCMs

Comparison of new and existing CCM construction techniques

Abstract

We characterize group symmetries of poly-phase complementary code matrices (CCMs), which we use to classify CCMs in terms of their equivalence classes. We also present classification results for CCMs of dimension $N\times 4$ where $N=2,3,4,5,6$. Finally, we present a new construction to generate quad-phase CCMs from ternary CCMs and compare this to other existing constructions that focus on generating CCMs from those of smaller dimensions.