Old and new families of strong Skolem Starters

Abstract

In this paper, we give new families of strong Skolem starters for ${\mathbb{Z}}_{p^n}$ and ${\mathbb{Z}}_{pq}$, for infinitely many odd primes $p,q\equiv 1$ (mod 8) and $n>1$ be an integer.

The paper gives an alternative (simple) construction of strong Skolem starters for ${\mathbb{Z}}_{p^n}$ and ${\mathbb{Z}}_{pq}$, for infinitely many odd primes $p,q\equiv 1$ (mod 8) and $n>1$ be an integer, than given by Ogandzhanyants et al. [O. Ogandzhanyants, M. Kondratieva, and N. Shalaby, \emph{Strong Skolem starters}, J. Combin. Des. {\bf 27} (2018), no. 1, 5--21]