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Algebraic Geometric codes on minimal Hirzebruch surfaces

Authors
  • Nardi, Jade
Publication Date
Jul 18, 2018
Source
HAL-UPMC
Keywords
Language
English
License
Unknown
External links

Abstract

We define a linear code by evaluating polynomials of bidegree in the Cox ring on Fq-rational points of a minimal Hirzebruch surface over the finite field Fq. We give explicit parameters of the code, notably using Gröbner bases. The minimum distance provides an upper bound of the number of Fq-rational points of a non-filling curve on a Hirzebruch surface.

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