**Author(s): ** Caleb McKinley Shor**Journal: ** Albanian Journal of Mathematics ISSN 1930-1235

**Volume: ** 5;

**Issue: ** 1;

**Start page: ** 31;

**Date: ** 2011;

Original page**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.

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