A class of cyclic $(v;k_1,k_2,k_3;\lambda)$ difference families with $v \equiv 3 \pmod{4}$ a prime

Abstract

We construct several cyclic $(v;k_1,k_2,k_3;\lambda)$ difference families with $v\equiv3 \pmod{4}$ a prime and $\lambda=k_1+k_2+k_3-(3v-1)/4$. Such families can be used in conjunction with the well-known Paley-Todd difference sets to construct skew-Hadamard matrices of order $4v$. Our main result is that we have constructed for the first time the example of skew-Hadamard matrices of orders $4\cdot239=956$ and $4\cdot331=1324$.