منابع مشابه
Weierstrass semigroups from Kummer extensions
The Weierstrass semigroups and pure gaps can be helpful in constructing codes with better parameters. In this paper, we investigate explicitly the minimal generating set of the Weierstrass semigroups associated with several totally ramified places over arbitrary Kummer extensions. Applying the techniques provided by Matthews in her previous work, we extend the results of specific Kummer extensi...
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Let E be an elliptic curve, and let Ln be the Kummer extension generated by a primitive pnth root of unity and a pn-th root of a for a fixed a ∈ Q − {±1}. A detailed case study by Coates, Fukaya, Kato and Sujatha and V. Dokchitser has led these authors to predict unbounded and strikingly regular growth for the rank of E over Ln in certain cases. The aim of this note is to explain how some of th...
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In the early eighties tools from algebraic geometry were applied by V. Goppa to construct linear codes using algebraic curves over finite fields, see [7]. Nowadays these codes are called algebraic-geometric codes, AG codes for short. The starting point in the construction of an AG code is a projective, absolutely irreducible, non singular algebraic curve X of genus g ≥ 1 defined over the finite...
متن کاملFactor Base Discrete Logarithms in Kummer Extensions
The discrete logarithm over finite fields of small characteristic can be solved much more efficiently than previously thought. This algorithmic breakthrough is based on pinpointing relations among the factor base discrete logarithms. In this paper, we concentrate on the Kummer extension Fq2(q−1) = Fq2 [x]/(x q−1 − A). It has been suggested that in this case, a small number of degenerate relatio...
متن کاملMulti-point codes over Kummer extensions
This paper is concerned with the construction of algebraic geometric codes defined from Kummer extensions. It plays a significant role in the study of such codes to describe bases for the Riemann-Roch spaces associated with totally ramified places. Along this line, we give an explicit characterization of Weierstrass semigroups and pure gaps. Additionally, we determine the floor of a certain typ...
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ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 1966
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-10774