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School of Mathematics and Statistics
Computational Algebra Group

Carslaw building

Algebra Seminar
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University of Sydney

School of Mathematics and Statistics

Computational Arithmetic Geometry Seminar

10:05 - 10.55 (+ epilogue until 11.30) in Carslaw 709 on Friday 28 February

Claus Fieker

Computing abelian extensions of global function fields

Quite a few of the known best codes come from global function fields or more presicely from function fields with many rational places in comparison with their genus. Most of the (theoretic) constructions for those fields are based on class field theory using either classical CFT (Ray class groups) or more modern approaches via Drinfeld modules.

In this talk I will demonstrate how the classcial approach can be used to compute defining equations for abelian extensions. The techniques are based on Kummer and Artin-Schreier-Witt theory, and follow the classical existence proofs.