Hadamard matrices with few distinct types

TL;DR

This paper explores Hadamard matrices with limited types of row quadruples, revealing that Sylvester Hadamard matrices can be characterized by their spectrum of types, aiding classification efforts.

Contribution

It introduces a novel approach to classify Hadamard matrices based on the spectrum of row quadruple types, especially characterizing Sylvester matrices.

Findings

Sylvester Hadamard matrices are characterized by their spectrum of types

Hadamard matrices with few distinct types are systematically investigated

Type classification aids in understanding Hadamard matrix structure

Abstract

The notion of type of quadruples of rows is proven to be useful in the classification of Hadamard matrices. In this paper, we investigate Hadamard matrices with few distinct types. Among other results, the Sylvester Hadamard matrices are shown to be characterized by their spectrum of types.