Algebraic Geometric codes from Kummer Extensions

Abstract

For Kummer extensions defined by $y^m=f(x)$, where $f(x)$ is a separable polynomial over the finite field ${\mathbb{F}}_q$, we compute the number of Weierstrass gaps at two totally ramified places. For many totally ramified places we give a criterion to find pure gaps at these points and present families of pure gaps. We then apply our results to construct many points algebraic geometric codes with good parameters.

16 pages

Cited by in corpus (2)

• Multi-point Codes over Kummer Extensions
• Weierstrass Pure Gaps From a Quotient of the Hermitian Curve