Hadamard matrices in $\{0,1\}$ presentation and an algorithm for generating them

TL;DR

This paper explores a zero-one presentation of Hadamard matrices and introduces an algorithm for generating these matrices based on this representation.

Contribution

The paper presents a novel approach to representing Hadamard matrices with zeros and ones, along with an original algorithm for their generation.

Findings

A new zero-one matrix representation of Hadamard matrices

An algorithm for generating Hadamard matrices from this representation

Potential applications in combinatorial design and coding theory

Abstract

Hadamard matrices are square $n\times n$ matrices whose entries are ones and minus ones and whose rows are orthogonal to each other with respect to the standard scalar product in $\Bbb R^n$. Each Hadamard matrix can be transformed to a matrix whose entries are zeros and ones. This presentation of Hadamard matrices is investigated in the paper and based on it an algorithm for generating them is designed.