Integer and Constraint Programming methods for Mutually Orthogonal Latin Squares
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منابع مشابه
Integrating Constraint and Integer Programming for the Orthogonal Latin Squares Problem
We consider the problem of Mutually Orthogonal Latin Squares and propose two algorithms which integrate Integer Programming (IP) and Constraint Programming (CP). Their behaviour is examined and compared to traditional CP and IP algorithms. The results assess the quality of inference achieved by the CP and IP, mainly in terms of early identification of infeasible subproblems. It is clearly illus...
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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...
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We show that k = w + 2 mutually unbiased bases can be constructed in any square dimension d = s provided that there are w mutually orthogonal Latin squares of order s. The construction combines the design-theoretic objects (k, s)-nets (which can be constructed from w mutually orthogonal Latin squares of order s and vice versa) and generalized Hadamard matrices of size s. Using known lower bound...
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It is known that t mutually orthogonal latin squares of order n generate a b t 2c-error correcting code with n codewords. In this paper we consider latin squares of order n made up of elements taken from Zn. In this situation we consider when this code is linear. We present neccessary and sufficient conditions on the latin squares and obtain a method of constructing a maximal family of mutually...
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Abstract. We show there is a natural connection between Latin squares and commutative sets of monomials defining geometric structures in finite phase-space of prime power dimensions. A complete set of such monomials defines a mutually unbiased basis (MUB) and may be associated with a complete set of mutually orthogonal Latin squares (MOLS). We translate some possible operations on the monomial ...
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تاریخ انتشار 2014