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Finite number of fibre products of Kummer covers and curves with many points over finite fields

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Abstract

We study fibre products of a finite number of Kummer covers of the projective line over finite fields. We determine the number of rational points of the fibre product over a rational point of the projective line, which improves the results of Özbudak and Temür (Appl Algebra Eng Commun Comput 18:433–443, 2007) substantially. We also construct explicit examples of fibre products of Kummer covers with many rational points, including a record and two new entries for the current table (http://www.manypoints.org, 2011).

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Authors and Affiliations

  1. Department of Mathematics and Institute of Applied Mathematics, Middle East Technical University, Dumlupınar Bulvarı, No: 1, 06800, Ankara, Turkey

    Ferruh Özbudak

  2. Department of Mathematics, Atılım University, İncek, Gölbaşı, 06836, Ankara, Turkey

    Burcu Gülmez Temür

Authors
  1. Ferruh Özbudak
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  2. Burcu Gülmez Temür
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Correspondence to Ferruh Özbudak.

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Communicated by G. Korchmaros.

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Özbudak, F., Gülmez Temür, B. Finite number of fibre products of Kummer covers and curves with many points over finite fields. Des. Codes Cryptogr. 70, 385–404 (2014). https://doi.org/10.1007/s10623-012-9706-2

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  • DOI: https://doi.org/10.1007/s10623-012-9706-2

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