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EXPLICIT TOWERS OF FUNCTION FIELDS OVER FINITE FIELDS

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Topics in Geometry, Coding Theory and Cryptography

Part of the book series: Algebra and Applications ((AA,volume 6))

Abstract

The purpose of this reviewarticle is to serve as an introduction and at the same time, as an invitation to the theory of towers of function fields over finite fields. More specifically, we treat here the case of explicit towers; i.e., towers where the function fields are given by explicit equations. The asymptotic behaviour of the genus and of the number of rational places in towers are important features for applications to coding theory and to cryptography (cf. Chapter 2).

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Authors
  1. Arnaldo Garcia
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  2. Henning Stichtenoth
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Editors and Affiliations

  1. Instituto de Matematica Pura e Aplicada (IMPA), Rio de Janeiro, Brazil

    Arnaldo Garcia

  2. University of Duisburg-Essen, Germany and Sabanci University, Istanbul, Turkey

    Henning Stichtenoth

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Garcia, A., Stichtenoth, H. (2006). EXPLICIT TOWERS OF FUNCTION FIELDS OVER FINITE FIELDS. In: Garcia, A., Stichtenoth, H. (eds) Topics in Geometry, Coding Theory and Cryptography. Algebra and Applications, vol 6. Springer, Dordrecht . https://doi.org/10.1007/1-4020-5334-4_1

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