Mutually Orthogonal Frequency Squares Obtained From Orthogonal Arrays

Orthogonal arrays are very useful. They are essential in statistics and they are usedin computer science and cryptography. Mutually orthogonal frequency squares (MOFSs),related to statistics, combinatorics and cryptography, are a generalization of mutuallyorthogonal Latin squares. This paper frstly presents an equivalence relation betweenMOFSs and a class of orthogonal arrays. Then, based on the equivalence relation, somenew methods for the construction of MOFSs are proposed and by using these methods,many lower bounds of MOFSs are improved. Some examples are given to illustrate theapplications of these methods.Chapter1introduces the development and the current research status of orthogonalarrays and MOFSs, and contains basic concepts and main lemmas.Chapter2mainly presents an equivalence relation between MOFSs and orthogonalarrays. By this relation, we know that some orthogonal arrays can be used to constructMOFSs, and conversely MOFSs provide a tool for constructing orthogonal arrays.Chapter3proposes four kinds of methods for constructing MOFSs from orthogonalarrays such as orthogonal decomposition of projection matrices, diference matrices, gen-eralized Kronecker product and generalized Hadamard product.In Chapter4, as an application of these methods proposed in Chapter3, a lot of newMOFSs are presented and compared with the existing results.Chapter5concludes the main content of this paper and puts forward some suggestionsand a few unsolved problems.