0000000001326957

AUTHOR

Alberto Picone

showing 5 related works from this author

New lower bounds for the minimum distance of generalized algebraic geometry codes

2013

Abstract In this paper, we give a new lower bound for generalized algebraic geometry codes with which we are able to construct some new linear codes having better parameters compared with the ones known in the literature. Moreover, we give a relationship between a family of generalized algebraic geometry codes and algebraic geometry codes. Finally, we propose a decoding algorithm for such a family.

Discrete mathematicsAlgebraic cycleBlock codeAlgebraic function field generalized algebraic geometry codes minimum distanceAlgebra and Number TheoryDerived algebraic geometryFunction field of an algebraic varietyAlgebraic surfaceReal algebraic geometryDimension of an algebraic varietySettore MAT/03 - GeometriaLinear codeMathematicsJournal of Pure and Applied Algebra
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On the classification of algebraic function fields of class number three

2012

AbstractLet F be an algebraic function field of one variable having a finite field Fq with q>2 elements as its field of constants. We determine all such fields for which the class number is three. More precisely, we show that, up to Fq-isomorphism, there are only 8 of such function fields. For q=2 the problem has been solved under the additional hypothesis that the function field is quadratic.

Discrete mathematicsAlgebraic function fieldFunction field of an algebraic varietyField (mathematics)Algebraic number fieldAlgebraic function fieldTheoretical Computer ScienceCombinatoricsDiscriminant of an algebraic number fieldField extensionDiscrete Mathematics and CombinatoricsQuadratic fieldAlgebraic functionSettore MAT/03 - GeometriaMathematicsClass numberDiscrete Mathematics
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Automorphisms of hyperelliptic GAG-codes

2009

Abstract We determine the n –automorphism group of generalized algebraic-geometry codes associated with rational, elliptic and hyperelliptic function fields. Such group is, up to isomorphism, a subgroup of the automorphism group of the underlying function field.

Abelian varietyDiscrete mathematicsautomorphismsGroup (mathematics)Applied Mathematicsgeneralized algebraic geometry codes.Outer automorphism groupReductive groupAutomorphismTheoretical Computer ScienceCombinatoricsMathematics::Group Theorygeometric Goppa codeAlgebraic groupDiscrete Mathematics and Combinatoricsalgebraic function fieldsSettore MAT/03 - GeometriaIsomorphismfinite fieldsGeometric Goppa codesfinite fieldalgebraic function fieldHyperelliptic curvegeneralized algebraic-geometry codesMathematicsDiscrete Mathematics
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Automorfismi di Codici Algebrico-Geometrici Generalizzati

2008

In questo lavoro si studiano gli automorfismi di codici algebrico geometrici generalizzati costruiti a partire da campi di funzione razionali, ellittici o iperellittici.

Codici algebrico geometriciSettore MAT/03 - Geometriacampi finitiposticampi di funzione
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Automorphisms of Hyperelliptic GAG-codes

2008

In this talk, we discuss the n-automorphism groups of generalized algebraic-geometry codes associated with rational, elliptic and hyperelliptic function fields. Such groups are, up to isomorphism, subgroups of the automorphism groups of the underlying function fields. We also present some examples in which the n-automorphism groups can be determined explicitly.

Automorphisms CodesSettore MAT/03 - Geometria
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