Constructing Pandiagonal Latin Squares from Linear Cellular Automaton on Elementary Abelian Groups

Abstract

The constructed pandiagonal Latin squares by Hedayat's method are cyclic. During the last decades several authors described methods for constructing pandiagonal Latin squares that are semi-cyclic. In this article, we have applied linear cellular automaton on elements of permutation elementary abelian p-groups, which are ordered by the lexicographic ordering, and we proposed an algorithm for constructing noncyclic pandiagonal Latin squares of order p α , for prime p ≥ 5.