Weighted perfect codes in Lee metric |
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| Affiliation: | 1. Laboratoire de Recherche en Informatique, Université Paris Sud, Orsay, 91405, France;2. ERT É "Maths à modeler", Institut Fourier, 100 rue des maths, BP74 38402 Saint Martin d''Hères, France;3. Department of Mathematics, University of Turku, FI-20014 Turku, Finland;1. Laboratoire de Recherche en Informatique, Université Paris Sud, Orsay, 91405, France;2. ERT É "Maths à modeler", Institut Fourier, 100 rue des maths, BP74 38402 Saint Martin d''Hères, France;3. Department of Mathematics, University of Turku, FI-20014 Turku, Finland;1. Department of Information Science, Faculty of Science, Toho University, Miyama 2-2-1, Funabashi, Chiba 274-8510, Japan;2. Bioinformatics Center, Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan |
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| Abstract: | In this talk, we will present results about perfect weighted coverings of radius 1 in the Lee metric. Weighted coverings are a very natural generalization of many classes of codes. Perfect weighted coverings are well studied in the Hamming metric, but also in other contexts with different names, such as regular-sets, multiple coverings or [a, b]-dominating sets. In this talk, we present results of existence as well as of non-existence for perfect weighted coverings of radius one on the multidimensional grid graphs. |
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