First explicit construction of quaternary Legendre pair length 64
A Quaternary Legendre Pair of Length 64
Discrete Mathematics
Summary
The paper presents a method to construct a special pair of sequences called a quaternary Legendre pair, each sequence having 64 elements. Such pairs are important in areas like signal processing because they have ideal correlation properties useful for reducing noise. Before this work, no explicit example of these pairs at length 64 was known. The authors provide the first concrete example, helping advance the study and potential applications of these sequences.
What this means in practice
- •For signal processing engineers: Improve signal clarity by using length 64 quaternary Legendre pairs for noise-resistant communication codes.
- •For communication system designers: Design longer, more reliable sequences for synchronization and spread spectrum protocols using the new 64-length quaternary Legendre pairs.
Authors
Harshit Verma
Abstract
We construct an explicit quaternary Legendre pair of length $64$. To the best of our knowledge, this is the first reported construction at this length.