# Skew-Hadamard matrices of orders 188 and 388 exist

## TL;DR

This paper presents the first construction of skew-Hadamard matrices of orders 188 and 388 using difference families on cyclic groups and the Goethals-Seidel array, expanding the known classes of such matrices.

## Contribution

First-time construction of skew-Hadamard matrices of orders 188 and 388 via difference families on cyclic groups and the Goethals-Seidel array.

## Key findings

- Constructed difference families on cyclic groups of orders 47 and 97.
- Successfully constructed skew-Hadamard matrices of orders 188 and 388.
- Matrices are constructed for the first time in this work.

## Abstract

We construct several difference families on cyclic groups of orders 47 and 97, and use them to construct skew-Hadamard matrices of orders 188 and 388. Such difference families and matrices are constructed here for the first time. The matrices are constructed by using the Goethals-Seidel array.