Bounds on (n,r)-arcs and their application to linear codes

  • Authors:
  • S. Ball;J. W. P. Hirschfeld

  • Affiliations:
  • Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, Jordi Girona 1-3, Mòdul C3, Campus Nord, 08034 Barcelona, Spain;Department of Mathematics, University of Sussex, Brighton BN1 9RF, UK

  • Venue:
  • Finite Fields and Their Applications
  • Year:
  • 2005

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Abstract

This article reviews some of the principal and recently-discovered lower and upper bounds on the maximum size of (n,r)-arcs in PG(2,q), sets of n points with at most r points on a line. Some of the upper bounds are used to improve the Griesmer bound for linear codes in certain cases. Also, a table is included showing the current best upper and lower bounds for q=