An Approach to the Bases of Riemann-Roch Spaces

Chuangqiang Hu () and Shudi Yang ()
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Chuangqiang Hu: Yanqi Lake Beijing Institute of Mathematical Sciences and Applications
Shudi Yang: Qufu Normal University

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 4, 1239-1248

Abstract: 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.

Keywords: Riemann-Roch space; Function field; AG code; 11R58; 14H55; 94B27 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00337-3

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