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An Approach to the Bases of Riemann-Roch Spaces

Author

Listed:
  • Chuangqiang Hu

    (Yanqi Lake Beijing Institute of Mathematical Sciences and Applications)

  • Shudi Yang

    (Qufu Normal University)

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.

Suggested Citation

  • Chuangqiang Hu & Shudi Yang, 2023. "An Approach to the Bases of Riemann-Roch Spaces," Indian Journal of Pure and Applied Mathematics, Springer, vol. 54(4), pages 1239-1248, December.
    • Handle: RePEc:spr:indpam:v:54:y:2023:i:4:d:10.1007_s13226-022-00337-3
    DOI: 10.1007/s13226-022-00337-3
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