Genus Calculations for Towers of Function Fields Arising From Equations of Cab Curves

Authors

Caleb Shor, Western New England UniversityFollow

College

College of Arts and Sciences

Department

Mathematics

Publication Date

2011

Abstract

We give a generalization of error-correcting code construction from C_ab curves by working with towers of algebraic function fields. The towers are constructed recursively, using defining equations of C_ab curves. In order to estimate the parameters of the corresponding one-point Goppa codes, one needs to calculate the genus. Instead of using the Hurwitz genus formula, for which one needs to know about ramification behavior, we use the Riemann-Roch theorem to get an upper bound for the genus by counting the number of Weierstrass gap numbers associated to a particular divisor. We provide a family of examples of towers which meet the bound.

Recommended Citation

Shor, Caleb, "Genus Calculations for Towers of Function Fields Arising From Equations of Cab Curves" (2011). Faculty Publications - College of Arts and Sciences. 23.
https://digitalcommons.law.wne.edu/casfacpubs/23