Algebraic Geometric codes from Kummer Extensions

2016/06/13 by Daniele Bartoli, Bartoli, Daniele, Luciane Quoos +3 · 1 citation
Computer Science · Mathematics · Medicine · #Coding theory and cryptography #Finite Group Theory Research #Cancer Mechanisms and Therapy

paper · pdf · doi:10.48550/arxiv.1606.04143

Abstract

For Kummer extensions defined by y^m = f (x), where f (x) is a separable polynomial over the finite field \mathbbF_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.

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• Pure Gaps at Many Places and Multi-point AG Codes from Arbitrary Kummer Extensions

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