A Class of Orthogonal Sequences

TL;DR

This paper introduces a new class of random orthogonal sequences derived from the number theoretic Hilbert transform, with potential cryptographic applications due to their autocorrelation properties.

Contribution

It provides a constructive method to generate these sequences for various moduli, expanding the toolkit for cryptography and signal processing.

Findings

Sequences have zero autocorrelation except at the origin

Constructive procedure for different moduli

Potential use as cryptographic keys

Abstract

This paper presents a class of random orthogonal sequences associated with the number theoretic Hilbert transform. We present a constructive procedure for finding the random sequences for different modulus values. These random sequences have autocorrelation function that is zero everywhere excepting at the origin. These sequences may be used as keys and in other cryptography applications.