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Arcs in AG(2, q) determining few directions

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Abstract

The study of k-arcs in AG(2, q) determining few directions is motivated by applications to secret sharing schemes. In this paper we obtain some new results for odd q. An essential tool comes from algebraic geometry via Segre’s result on algebraic envelopes associated to a k-arc.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli, 1, 06123, Perugia, Italy

    Massimo Giulietti

  2. Dipartimento di Matematica e Informatica, Università della Basilicata, Contrada Macchia Romana, 85100, Potenza, Italy

    Gábor Korchmáros

Authors
  1. Massimo Giulietti
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  2. Gábor Korchmáros
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Correspondence to Massimo Giulietti.

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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Finite Geometries”.

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Giulietti, M., Korchmáros, G. Arcs in AG(2, q) determining few directions. Des. Codes Cryptogr. 68, 61–72 (2013). https://doi.org/10.1007/s10623-012-9630-5

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  • DOI: https://doi.org/10.1007/s10623-012-9630-5

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