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A Tutorial on AG Code Construction from a Gröbner Basis Perspective

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Gröbner Bases, Coding, and Cryptography

Abstract

This chapter is meant primarily as an introduction to AG codes, with material on producing proper one-point descriptions of these codes as well. The terminology chosen is that of the easily understood concepts of multivariate polynomial rings and ideals of relations among the variables, which is more useful computationally than the more standard algebraic geometry terminology.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Auburn University, Auburn, AL, 36849, USA

    Douglas A. Leonard

Authors
  1. Douglas A. Leonard
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Corresponding author

Correspondence to Douglas A. Leonard .

Editor information

Editors and Affiliations

  1. Boole Centre for Research in Informatics, University College Cork, Crosses Green 17 South Bank, Cork, Ireland

    Massimiliano Sala

  2. Faculty of Engineering Dept. Production Systems Engineering, Toyohashi University of Technology, 1-1 Hibarigaoka Toyohashi, Aichi, Tempaku-cho, 441-8580, Japan

    Shojiro Sakata

  3. Dipto. Matematica, Università Genova, Via Dodecaneso, 35, 16146, Genova, Italy

    Teo Mora

  4. Dipto. Matematica, Università Pisa, Largo Bruno Pontecorvo, 5, 56127, Pisa, Italy

    Carlo Traverso

  5. LIP6, University of Paris VI, 104 avenue du Président Kennedy, 75016, Paris, France

    Ludovic Perret

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© 2009 Springer-Verlag Berlin Heidelberg

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Leonard, D.A. (2009). A Tutorial on AG Code Construction from a Gröbner Basis Perspective. In: Sala, M., Sakata, S., Mora, T., Traverso, C., Perret, L. (eds) Gröbner Bases, Coding, and Cryptography. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-93806-4_6

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