A Construction of Special Self-Orthogonal Latin Squares Based on Frequency Squares

Abstract

Let $n=p^k$, where $p$ is a prime and $k\ge 2.$ In this paper, a construction for weakly pandiagonal strongly symmetric self-orthogonal diagonal Latin squares of order $n$ is given by using frequency squares over finite field of order $p.$\u00a0It is proved that there exists a weakly pandiagonal strongly symmetric selforthogonal diagonal Latin square of order $n$ for $n> 4.$