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Informationen zum Autor Simeon Ball is a senior lecturer in the Department of Applied Mathematics IV at Universitat Politècnica de Catalunya, Barcelona. He has published over 50 articles and been awarded various prestigious grants, including the Advanced Research Fellowship from EPSRC in the UK and the Ramon y Cajal grant in Spain. In 2012 he proved the MDS conjecture for prime fields, which conjectures that all linear codes over prime fields that meet the Singleton bound are short. This is one of the oldest conjectures in the theory of error-correcting codes. Klappentext A graduate-level introduction to finite geometry and its applications to other areas of combinatorics. Zusammenfassung For students and researchers interested in algebraic combinatorics! this book not only provides an introduction to the geometries arising from vector spaces over finite fields but also shows how these geometries can be applied to various combinatorial objects. More than 100 exercises and solutions are provided. Inhaltsverzeichnis 1. Fields; 2. Vector spaces; 3. Forms; 4. Geometries; 5. Combinatorial applications; 6. The forbidden subgraph problem; 7. MDS codes; Appendix A. Solutions to the exercises; Appendix B. Additional proofs; Appendix C. Notes and references; References; Index.
