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- W2807776107 abstract "A difference matrix over a group is a discrete structure that is intimately related to many other combinatorial designs, including mutually orthogonal Latin squares, orthogonal arrays and transversal designs. Interest in constructing difference matrices over 2-groups has been renewed by the recent discovery that these matrices can be used to construct large linking systems of difference sets, which in turn provide examples of systems of linked symmetric designs and association schemes. We survey the main constructive and nonexistence results for difference matrices, beginning with a classical construction based on the properties of a finite field. We then introduce the concept of a contracted difference matrix, which generates a much larger difference matrix. We show that several of the main constructive results for difference matrices over abelian p-groups can be substantially simplified and extended using contracted difference matrices. In particular, we obtain new linking systems of difference sets of size 7 in infinite families of abelian 2-groups, whereas previously the largest known size was 3." @default.
- W2807776107 created "2018-06-21" @default.
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- W2807776107 date "2019-07-08" @default.
- W2807776107 modified "2023-09-23" @default.
- W2807776107 title "6. A new structure for difference matrices over abelian p-groups" @default.
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- W2807776107 doi "https://doi.org/10.1515/9783110642094-006" @default.
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