A latin square with orthogonal mate and no automorphism

A class of orthogonal latin square graphs

An orthogonal latin square graph is a graph whose vertices are latin squares of the same order, adjacency being synonymous with orthogonality. We are interested in orthogonal latin square graphs in which each square is orthogonal to the Cayley table M of a group G and is obtained from M by permuting columns. These permutations, regarded as permutations of G, are orthomorphisms of G and the grap...

Representations of graphs and orthogonal latin square graphs

We define graph representations modulo integers and prove that any finite graph has a representation modulo some integer. We use this to obtain a new, simpler proof of Lindner, E. Mendelsohn, N. Mendelsohn, and Wolk’s result that any finite graph can be represented as an orthogonal latin square graph. Let G be a graph with vertices v,, . . . , u, and let n be a natural number. We say that G is ...

Error Correction Using Extended Orthogonal Latin Square Codes

To protect memories against errors, error correction codes (ECCs) are used. As frequency of occurring multiple errors are common, we need to go for advanced ECCs. Among advanced ECCs, Orthogonal Latin Squares (OLS) codes have gained renewed interest for memory protection due to their modularity and the simplicity of the decoding algorithm that enables low delay implementations. An important iss...

Square-free Rings and Their Automorphism Group

Finite-dimensional square-freeK-algebras have been completely characterized by Anderson and D’Ambrosia as certain semigroup algebras A ∼= KξS over a square-free semigroup S twisted by some ξ ∈ Z (S,K), a two-dimensional cocycle of S with coefficients in the group of units K∗ of K. D’Ambrosia extended the definition of square-free to artinian rings with unity and showed every square-free ring ha...

An Application of Sum Composition: A Self Orthogonal Latin Square of Order Ten