Weierstrass Semigroups From a Tower of Function Fields Attaining the Drinfeld-Vladut Bound

2019/11/07 by Shudi Yang, Yang, Shudi, Chuangqiang Hu +1 · 1 citation
Computer Science · Mathematics · #11R58 #14H55 #94B27 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Coding theory and cryptography #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1911.04269

openalex publication_date 2019/11/07 · openalex created_date 2019/11/22 · openalex updated_date 2026/07/28

Abstract

For applications in algebraic geometric codes, an explicit description of bases of Riemann-Roch spaces of divisors on function fields over finite fields is needed. We investigate the third function field F⁽³⁾ in a tower of Artin-Schreier extensions described by Garcia and Stichtenoth reaching the Drinfeld-Vlăduţ bound. We construct bases for the related Riemann-Roch spaces on F⁽³⁾ and present some basic properties of divisors on a line. From the bases, we explicitly calculate the Weierstrass semigroups and pure gaps at several places on F⁽³⁾ . All of these results can be viewed as a generalization of the previous work done by Voss and Høholdt (1997).

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