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

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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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Journal articles
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Cited literature [26 references]

https://hal.archives-ouvertes.fr/hal-02411489
Contributor : Elena Berardini Connect in order to contact the contributor
Submitted on : Sunday, March 1, 2020 - 12:21:59 PM
Last modification on : Thursday, August 4, 2022 - 4:59:21 PM
Long-term archiving on: : Sunday, May 31, 2020 - 12:27:19 PM

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### Citation

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, ⟨10.1090/conm/770⟩. ⟨hal-02411489v3⟩

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