0000000000875514

AUTHOR

Alberto Picone

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

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.

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Automorfismi di Codici Algebrico-Geometrici Generalizzati

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

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On the classification of algebraic function fields of class number three

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.

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Automorphisms of hyperelliptic GAG-codes

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.

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Automorphisms of Hyperelliptic GAG-codes

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.

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