Skew-Hadamard matrices of orders 436, 580 and 988 exist

TL;DR

This paper presents the first construction of skew-Hadamard matrices of orders 436, 580, and 988 using difference families on cyclic groups and the Goethals-Seidel array, expanding the known existence of such matrices.

Contribution

First-time construction of skew-Hadamard matrices of orders 436, 580, and 988 via difference families and Goethals-Seidel array.

Findings

Constructed difference families on cyclic groups of orders 109, 145, 247

Built skew-Hadamard matrices of orders 436, 580, 988 for the first time

Demonstrated the use of Goethals-Seidel array in these constructions

Abstract

We construct two difference families on each of the cyclic groups of order 109, 145 and 247, and use them to construct skew-Hadamard matrices of orders 436, 580 and 988. Such difference families and matrices are constructed here for the first time. The matrices are constructed by using the Goethals-Seidel array.