2023/11/17 by Alonso S. Castellanos, Castellanos, Alonso S., Erik A. R. Mendoza +3 · 1 citation
Computer Science · Biochemistry, Genetics and Molecular Biology · #Coding theory and cryptography #semigroups and automata theory #DNA and Biological Computing
paper · pdf · doi:10.48550/arxiv.2311.10477
In this work, using maximal elements in generalized Weierstrass semigroups and its relationship with pure gaps, we extend the results in \citeCMT2024 and provide a way to completely determine the set of pure gaps at several rational places in an arbitrary function field F over a finite field and its cardinality. As an example, we determine the cardinality and a simple explicit description of the set of pure gaps at several rational places distinct to the infinity place on Kummer extensions, which is a different characterization from that presented by Hu and Yang in \citeHY2018. Furthermore, we present some applications in coding theory and AG codes with good parameters.