Hadamard matrices from base sequences: An example

TL;DR

This paper demonstrates the prolific use of various methods to construct a large number of non-equivalent Hadamard matrices of order 60 from base sequences, highlighting the richness of these construction techniques.

Contribution

It provides an explicit example of generating 1759 non-equivalent Hadamard matrices of order 60 using known methods and the transposition map.

Findings

Constructed 1759 non-equivalent Hadamard matrices of order 60.

Showcases the effectiveness of existing methods and transposition in generating diverse matrices.

Highlights the abundance of Hadamard matrices obtainable from base sequences.

Abstract

There are several well-known methods that one can use to construct Hadamard matrices from base sequences BS(m,n). In view of the recent classification of base sequences BS(n+1,n) for n <= 30, it may be of interest to show on an example how prolific these methods are. For that purpose we have selected the Hadamard matrices of order 60. By using these methods and the transposition map we have constructed 1759 nonequivalent Hadamard matrices of order 60.