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An Approach to the Bases of Riemann-Roch Spaces

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Abstract

For applications in algebraic geometric codes, it is extremely useful to give an explicit description of the bases of Riemann-Roch spaces associated to divisors on function fields over finite fields. We demonstrate a general approach to construct such a monomial basis for the related Riemann-Roch space. More precisely we present a criterion for finding an explicit basis for the Riemann-Roch space of a three-point divisor. Furthermore, we improve an upper bound for the genus of the related function field. Some examples are also given to illustrate our general approach.

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Authors and Affiliations

  1. Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Peking, 101408, P R China

    Chuangqiang Hu

  2. School of Mathematical Sciences, Qufu Normal University, Shandong, 273165, P R China

    Shudi Yang

Authors
  1. Chuangqiang Hu
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  2. Shudi Yang
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Correspondence to Shudi Yang.

Additional information

Communicated by Sudhir R. Ghorpade

The second affiliation has been updated.

This work is partly supported by the National Natural Science Foundation of China under Grants 12071247 and 12101616.

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Hu, C., Yang, S. An Approach to the Bases of Riemann-Roch Spaces. Indian J Pure Appl Math 54, 1239–1248 (2023). https://doi.org/10.1007/s13226-022-00337-3

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