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Pré-Publication, Document De Travail Année : 2020

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. What characterizes the bounds we obtain is that they involve a measure of closeness of the divisor defining the code to the ample cone in the Néron-Severi group.
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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. 2020. ⟨hal-02411489v2⟩
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