We introduce orthogonal quantum Latin squares, which restrict to traditional orthogonal Latin squares, and investigate their application in quantum information science. We use quantum Latin squares to build maximally entangled bases, and show how mutually unbiased maximally entangled bases can be constructed in square dimension from orthogonal quantum Latin squares. We also compare our construc...

A critical set is a partial latin square that has a unique completion to a latin square of the same order, and is minimal in this property. If P is a critical set in a latin square L, then each element of P must be contained in a latin trade Q in L such that |P ∩ Q| = 1. In the case where each element of P is contained in an intercalate (latin trade of size 4) Q such that |P∩Q| = 1 we say that ...

The problem of obtaining network coding maps for the physical layer network coded two-way relay channel is considered, using the denoise-and-forward forward protocol. It is known that network coding maps used at the relay node which ensure unique decodability at the end nodes form Latin Squares. Also, it is known that minimum distance of the effective constellation at the relay node becomes zer...

IsotoIHsl:n that lower bounds for infinite N of order n. hand or computer, strong critical sets of minimum nOn-lS01110Tnitnc reduced latin squares of order less than or of order 6. These latin squares have been taken from 129 onwards. We summarise our results in Table the numbering system listed by Denes and Keedwell latin squares. This numbering system is based on the ,<:n,,-r1i',rrHl1<:rn cla...

In an attempt to classify all of the overlap-free morphisms constructively using the Latin-square morphism, we came across an interesting counterexample, the Leech square-free morphism. We generalize the combinatorial properties of the Leech square-free morphism to gain insights on a larger class of both overlap-free morphisms and square-free morphisms.

A row-complete Latin square (RCLS) of order n, L, is a Latin square in which for any two distinct symbols, X, y, there exist i, j, 1 <i < ~1, 1 <:j < n 1 such that L(i,j) k x and L(i,j I1) =y. Column complete Latin squares are defmed analogously, and a square is complete if it is both. row and column complete. RCLS are used in statistics for the design of sequential experiments. A finite group ...