The set of pure gaps at several rational places in function fields

The article delves into the set of pure gaps at several rational places in function fields, a fundamental topic in algebraic geometry and coding theory. It builds on classic research by introducing a method to completely determine the set of pure gaps and their cardinality. This work is particularly notable for its applications in coding theory, where it provides a framework for constructing AG codes with better parameters. The study also includes a detailed outline of the paper, presenting basic results, terminologies, and an explicit description of the pure gap set in terms of relative maximal elements. The authors conclude with applications in coding theory, demonstrating the construction of differential AG codes with improved relative parameters over Kummer extensions. The article is a must-read for researchers interested in the intersection of algebraic geometry and coding theory, offering both theoretical insights and practical applications.