On Weighted-Sum Orthogonal Latin Squares and Secret Sharing

Latin squares are a classical and well-studied topic of discrete mathematics, and recently Takeuti and Adachi (IACR ePrint, 2023) proposed (2 , n)-threshold secret sharing based on mutually orthogonal Latin squares (MOLS). Hence efficient constructions of as large sets of MOLS as possible are also important from practical viewpoints. In this letter, we determine the maximum number of MOLS among a known class of Latin squares defined by weighted sums. We also mention some known property of Latin squares interpreted via the relation to secret sharing and a connection of Takeuti-Adachi's scheme to Shamir's secret sharing scheme.