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Finite Geometry and Combinatorial Applications
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    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Chen, Bocong and Liu, Hongwei 2018. New Constructions of MDS Codes With Complementary Duals. IEEE Transactions on Information Theory, Vol. 64, Issue. 8, p. 5776.

    Bartoli, D. Davydov, A. A. Marcugini, S. and Pambianco, F. 2018. On the Smallest Size of an Almost Complete Subset of a Conic in PG(2, q) and Extendability of Reed–Solomon Codes. Problems of Information Transmission, Vol. 54, Issue. 2, p. 101.

    Ball, Simeon 2018. Extending small arcs to large arcs. European Journal of Mathematics, Vol. 4, Issue. 1, p. 8.

    Hua, Michael Damelin, Steven B. Sun, Jeffrey and Yu, Mingchao 2018. The truncated and supplemented Pascal matrix and applications. Involve, a Journal of Mathematics, Vol. 11, Issue. 2, p. 243.

    Ball, Simeon and De Beule, Jan 2017. On Subsets of the Normal Rational Curve. IEEE Transactions on Information Theory, Vol. 63, Issue. 6, p. 3658.

  • Simeon Ball, Universitat Politècnica de Catalunya, Barcelona

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Book description

The projective and polar geometries that arise from a vector space over a finite field are particularly useful in the construction of combinatorial objects, such as latin squares, designs, codes and graphs. This book provides an introduction to these geometries and their many applications to other areas of combinatorics. Coverage includes a detailed treatment of the forbidden subgraph problem from a geometrical point of view, and a chapter on maximum distance separable codes, which includes a proof that such codes over prime fields are short. The author also provides more than 100 exercises (complete with detailed solutions), which show the diversity of applications of finite fields and their geometries. Finite Geometry and Combinatorial Applications is ideal for anyone, from a third-year undergraduate to a researcher, who wishes to familiarise themselves with and gain an appreciation of finite geometry.

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