Browsing by Subject "Algebraic curve"
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Item Open Access Character sums, algebraic function fields, curves with many rational points and geometric Goppa codes(1997) Özbudak, FerruhIn this thesis we have found and studied fibre products of hyperelliptic and superelliptic curves with many rational points over finite fields. We have applied Goppa construction to these curves to get “good” linear codes. We have also found a nontrivial connection between configurations of affine lines in the affine plane over finite fields and fibre products of Rummer extensions giving “good” codes over F,2. Moreover we have calculated an important parameter of a class of towers of algebraic function fields over finite fields, which are studied recently.Item Open Access A Divisibility theorem for the Alexander polynomial of a plane algebraic curve(Springer New York LLC, 2004) Degtyarev, A. I.An upper estimate for the Alexander polynomial of an algebraic curve is obtained, which sharpens Libgober's estimate in terms of the local polynomials at the singular points of the curve: only those singular points may contribute to the Alexander polynomial of the curve that are in the excess of the hypothesis of Nori's vanishing theorem.