This paper proposes a method for exhaustively generating all pairs of linear cellular automata, specifically Orthogonal Cellular Automata (OCA), that give rise to orthogonal Latin squares. The primary challenge addressed involves enumerating pairs of coprime polynomials over a finite field, having the same degree and a nonzero constant term. This effort yields insights into algebraic language theory and combinatorics, offering an enumeration algorithm and an alternative derivation of the counting formula for this problem. The applications of these OCAs span cryptography and coding theory, implying practical utility for the study.
Publication date: July 17, 2023
Project Page: N/A
Paper: https://arxiv.org/pdf/2307.07505.pdf
