Bounds on the minimum distance of algebraic geometry codes defined over some families of surfaces - Institut de Mathématiques de Luminy
Article Dans Une Revue Contemporary mathematics Année : 2021

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

Résumé

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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Dates et versions

hal-02411489 , version 1 (16-12-2019)
hal-02411489 , version 2 (01-02-2020)
hal-02411489 , version 3 (01-03-2020)

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Yves Aubry, Elena Berardini, Fabien Herbaut, Marc Perret. Bounds on the minimum distance of algebraic geometry codes defined over some families of surfaces. Contemporary mathematics, 2021, 770, ⟨10.48550/arXiv.1912.07450⟩. ⟨hal-02411489v3⟩
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