An application of difference sets to a problem concerning graphical codes |
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| Institution: | 1. Lehrstuhl für Angewandte Mathematik II, Universität Augsburg, D-86135 Augsburg, Germany;2. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ont., Canada N2L 3G1;1. Department of Earth and Environmental Sciences, Ludwig-Maximilians-Universität München, Theresienstr. 41, 80333, Munich, Germany;2. Experimental Physics II, Universität Augsburg, Universitätsstr. 1, 86159, Augsburg, Germany;1. Department of Radiology, Medical Physics, Medical Center, University of Freiburg, Faculty of Medicine, University of Freiburg, Germany;2. Department of Diagnostic and Interventional Radiology and Neuroradiology, Augsburg Hospital, Germany;3. Department of Neuroradiology, Medical Center – University of Freiburg, Faculty of Medicine, University of Freiburg, Germany;1. Institut de Mathématiques de Jussieu, CNRS–UMR 7586, 4 Place Jussieu, 75 005 Paris, France;2. Université Pierre et Marie Curie - P6, 4 Place Jussieu, 75 005 Paris, France;3. Centre for Mathematical Sciences, and Institute for Advanced Study, Technische Universität München, Boltzmannstrasse 3, 85748 Garching, Germany;4. Institute for Mathematics, Universität Augsburg, Universitätsstraße 14, 86159 Augsburg, Germany |
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| Abstract: | By using difference sets, we give an answer to the following problem concerning graphical codes: When is the binary code generated by the complete graph Kn contained in some binary Hamming code? It turns out that this holds if and only if n is one of the numbers 2, 3 and 6. |
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