Reconstructing Sets of Latin Squares, Linear and Equivalent to Linear Codes

We consider the reconstruction problem concerning latin squares, sets of mutually orthogonal latin squares as well as linear and equivalent to linear codes in a vector space over a finite field. With regard to this problem we discuss related topics on intersection of combinatorial objects of the same class. An algorithm reconstructing latin squares and its sets is presented. By this way it is shown for q ∈ {3, 4, 5, 7} that the Bose complete set of mutually orthogonal latin squares of order q with 2q - 1 or less blank entries in each square at the same places is reconstructed uniquely. We also point some recently obtained results on the maximum intersection of linear and equivalent to linear codes, and their applications as well.