Construction of symmetric Hadamard matrices of order $4v$ for $v=47,73,113$

TL;DR

This paper extends the search for symmetric Hadamard matrices using the propus construction to new orders, successfully finding matrices for specific values of v including 47, 73, and 113, thus advancing the classification of these matrices.

Contribution

It introduces new symmetric Hadamard matrices of order 4v for v=47, 73, and 113 using the propus construction, expanding known cases.

Findings

Found symmetric Hadamard matrices for v=47, 73, 113

Extended the known orders of symmetric Hadamard matrices

Demonstrated effectiveness of the propus construction

Abstract

We continue our systematic search for symmetric Hadamard matrices based on the so called propus construction. In a previous paper this search covered the orders $4v$ with odd $v\le41$. In this paper we cover the cases $v=43,45,47,49,51$. The odd integers $v<120$ for which no symmetric Hadamard matrices of order $4v$ are known are the following: $$47,59,65,67,73,81,89,93,101,103,107,109,113,119.$$ By using the propus construction, we found several symmetric Hadamard matrices of order $4v$ for $v=47,73,113$.