Klein-4 Group of Constructing Distinct Sets of Mutually Orthogonal Latin Squares of Order

A. J.  Saka; R. A.  Adetona; T. J.  Awe; T. G.  Jaiyeola; K. A.  Olurode; K.  Odizilike

doi:10.5281/zenodo.20466858

A. J. Saka Department of Statistics, Obafemi Awolowo University, Ile Ife 220005, Nigeria.
R. A. Adetona Department of Statistics, Obafemi Awolowo University, Ile Ife 220005, Nigeria.
T. J. Awe Department of Mathematics, Obafemi Awolowo University, ile-ife
T. G. Jaiyeola Department of Mathematics, University of Lagos, Akoka 101017, Nigeria.
K. A. Olurode
K. Odizilike Department of Statistics, Obafemi Awolowo University, Ile Ife 220005, Nigeria.

DOI: https://doi.org/10.5281/zenodo.20466858

Keywords: Latin squares, Mutually orthogonal latin squares, Symmetric group, Klein-4 group.

Abstract

The concept of mutually orthogonal Latin squares (MOLS) have been studied extensively since Euler's pioneering work in 1782. The construction of MOLS of various orders have since been the subject of considerable research. Researchers have utilized different algebraic structures to construct MOLS, while some emphasized on matrices and maximal partial spreads in finite projective spaces. However, the basis of the aforementioned methods were the provision of systematic approach to ensure orthogonality. A new method of constructing distinct set of mutually orthogonal Latin squares (MOLS) of order 4 called Klein-4 Group is presented in this paper. Therein the symmetries of rectangle (isomorphic to Klein-4 group C2×C2C2×C2 ) is leveraged on to aid the construction of 4 distinct complete sets of MOLS. The design could open ways for its application in cryptography, generation of one time password (OPT) and in cyber environments such as Internet of Things (IoT) needing lightweight cybersecurity measures.

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