Existence of symmetric skew balanced starters for odd prime powers

Abstract:

Strong starters and skew starters have been widely used in various combinatorial designs. In particular skew balanced starters and symmetric skew balanced starters are crucially used in the construction of completely balanced Howell rotations. Let $n = {2^m}k + 1$ be an odd prime power where $m \geq 2$ and $k$ is an odd number. The existence of symmetric skew balanced starters for $GF(n)$ has been proved for $m \geq 2$ and $k \ne 1,3,9$. In this paper, we present a new approach which gives a uniform proof of the existence of symmetric skew balanced starters for all $m \geq 2$ and $k \geq 3$.