Search results for "algebraic function field"

showing 5 items of 5 documents

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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Asymptotically good codes from generalized algebraic-geometry codes

2005

We consider generalized algebraic-geometry codes, based on places of the same degree of a fixed algebraic function field over a finite field. In this note, using a method similar to the Justesen's one, we construct a family of such codes which is asymptotically good.

Algebraic function fieldBlock codeDiscrete mathematicsFunction field of an algebraic varietyApplied MathematicsReal algebraic geometryAlgebraic extensionAlgebraic functionLinear codeExpander codeComputer Science ApplicationsMathematics
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ON AUTOMORPHISMS OF GENERALIZED ALGEBRAIC-GEOMETRY CODES.

2007

Abstract We consider a class of generalized algebraic-geometry codes based on places of the same degree of a fixed algebraic function field over a finite field F / F q . We study automorphisms of such codes which are associated with automorphisms of F / F q .

Algebraic function fieldDiscrete mathematicsAlgebraic cycleFinite fieldFunction field of an algebraic varietyAlgebra and Number TheoryAutomorphisms of the symmetric and alternating groupsAlgebraic extensionAlgebraic geometryAutomorphismMathematics
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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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