Finite geometry and combinatorial applications
by Ball, Simeon, (Simeon Michael)
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 p…
Read More ↓Title Statements
- Full title :Finite geometry and combinatorial applications / Simeon Ball, Universitat Politècnica de Catalunya, Barcelona.
Summary
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.
Read More ↓Edition Statements
- Publication Date:2015.
Publication Statements
- Publisher(s):Cambridge University Press
- Place of Publication:Cambridge
- Language:eng
- Publication Date:2015.
The Physical Object
- Description:1 online resource (xii, 285 pages)
Edition Identifiers
- ISBN:9781316257449, 1316257444
- oclc:ocn915136558
- LC Classification:QA167.2
- Dewey Decimal:516/.11
Table of Contents
7.14 The algebraic hypersurface associated with a linear MDS code -- 7.15 Extendability of linear MDS codes -- 7.16 Classification of linear MDS codes of length q+1 for k< -- c√g -- 7.17 A proof of the MDS conjecture for k < -- c √q -- 7.18 Exercises -- Appendix A Solutions to the exercises -- A.1 Fields -- A.2 Vector spaces -- A.3 Forms -- A.4 Geometries -- A.5 Combinatorial applications -- A.6 The forbidden subgraph problem -- A.7 MDS codes -- Appendix B Additional proofs -- B.1 Probability -- B.2 Fields -- B.3 Commutative algebra -- Appendix C Notes and references -- C.1 Fields -- C.2 Vector spaces -- C.3 Forms -- C.4 Geometries -- C.5 Combinatorial applications -- C.6 The forbidden subgraph problem -- C.7 MDS codes -- C.8 Appendices -- References -- Index.
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