A doubling construction for Williamson matrices

TL;DR

This paper introduces a new constructive method to generate Williamson matrices of order 2n from those of odd order n, using only three simple sequence operations, advancing the algebraic construction techniques.

Contribution

It presents a novel, fully constructive doubling method for Williamson matrices that simplifies their generation process from odd to even order.

Findings

Provides a new doubling construction for Williamson matrices

Uses only three simple sequence operations

Enables generation of even order Williamson matrices from odd order ones

Abstract

A construction that generates Williamson matrices of order $2n$ from Williamson matrices of odd order $n$ is presented. The construction is completely constructive and only uses three simple sequence operations.