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

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, surfa...

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Bibliographic Details
Published inArithmetic, Geometry, Cryptography and Coding Theory Vol. 770; pp. 11 - 28
Main Authors Aubry, Yves, Berardini, Elena, Herbaut, Fabien, Perret, Marc
Format Book Chapter
LanguageEnglish
Published Providence, Rhode Island American Mathematical Society
SeriesContemporary Mathematics
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ISBN9781470454265
1470454262
ISSN0271-4132
1098-3627
DOI10.1090/conm/770/15428

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Summary: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
ISBN:9781470454265
1470454262
ISSN:0271-4132
1098-3627
DOI:10.1090/conm/770/15428