A \(p\)-adic Serre bound
The main result of this paper combines a technique due to Serre with the authors own improvement of results due to Ax and Katz to produce a general \(p\)-adic Serre bound. This improves and generalizes earlier results by the same authors. The work in the paper was motivated by coding theory and has immediate applications that give minimum distance estimates for cyclic codes. Motivated by algebraic geometric Goppa codes the authors estimate the number of rational points of complete intersections. The authors give a \(p\)-adic Serre bound for complete intersections and estimate the Betti number for a complete intersection.
minimum distance estimates for cyclic codes
number of rational points of complete intersections
scientific article; zbMATH DE number 1236196
scientific article