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arXiv · 1912.07450

Bounds on the minimum distance of algebraic geometry codes defined over some families of surfaces

Yves Aubry·Elena Berardini·Fabien Herbaut·Marc Perret
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Abstract

We prove lower bounds for the minimum distance of algebraic geometry codes over surfaces whose canonical divisor is either nef or anti-strictly nef and over surfaces without irreducible curves of small genus. We sharpen these lower bounds for surfaces whose arithmetic Picard number equals one, surfaces without curves with small self-intersection and fibered surfaces. Finally we specify our bounds to the case of surfaces of degree $d\geq 3$ embedded in $\mathbb{P)^3$.

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Yves Aubry, Elena Berardini, Fabien Herbaut, Marc Perret. 2019-12-16. Bounds on the minimum distance of algebraic geometry codes defined over some families of surfaces. https://arxiv.org/abs/1912.07450

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