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Finite geometry and combinatorial applications / Simeon Ball, Universitat Politècnica de Catalunya, Barcelona.

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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 a...

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Bibliographic Details
Online Access: Full Text (via Cambridge)
Main Author: Ball, Simeon (Simeon Michael) (Author)
Format: Electronic eBook
Language:English
Published: Cambridge : Cambridge University Press, 2015.
Series:London Mathematical Society student texts ; 82.
Subjects:
Finite geometries.
Combinatorial analysis.
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&lt
  • c√g
  • 7.17 A proof of the MDS conjecture for k &lt
  • 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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