A complementary construction using mutually unbiased bases

TL;DR

This paper introduces a new method for constructing complementary array pairs and sequences using mutually unbiased bases, providing a systematic generation algorithm and analyzing their correlation properties.

Contribution

It presents a novel construction leveraging mutually unbiased bases for complementary arrays and sequences, including an algorithm for unique sequence generation.

Findings

Sequence set pairwise squared inner-product is 1/2

A subset of sequences asymptotically reaches the Welch bound

Enumeration of arrays and sequences derived from the construction

Abstract

We present a construction for complementary pairs of arrays that exploits a set of mutually-unbiased bases, and enumerate these arrays as well as the corresponding set of complementary sequences obtained from the arrays by projection. We also sketch an algorithm to uniquely generate these sequences. The pairwise squared inner-product of members of the sequence set is shown to be $\frac{1}{2}$. Moreover, a subset of the set can be viewed as a codebook that asymptotically achieves $\sqrt{\frac{3}{2}}$ times the Welch bound.