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Your search keyword '"Absolutely irreducible"' showing total 2 results
2 results on '"Absolutely irreducible"'

1. The k-subset sum problem over finite fields.

Author

Wang, Weiqiong and Nguyen, Jennifer

Subjects
*SUBSET selection, *FINITE fields, *ALGEBRAIC fields, *ORDERED algebraic structures, *CODING theory, *CRYPTOGRAPHY, *GRAPH theory
Abstract

The subset sum problem is an important theoretical problem with many applications, such as in coding theory, cryptography, graph theory and other fields. One of the many aspects of this problem is to answer the solvability of the k -subset sum problem. It has been proven to be NP-hard in general. However, if the evaluation set has some special algebraic structure, it is possible to obtain some good conclusions. Zhu, Wan and Keti proposed partial results of this problem over two special kinds of evaluation sets. We generalize their conclusions in this paper, and propose asymptotical results of the solvability of the k -subset sum problem by using estimates of additive character sums over the evaluation set, together with the Brun sieve and the new sieve proposed by Li and Wan. We also apply the former two examples as application of our results. [ABSTRACT FROM AUTHOR]

Published
2018
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2. Coverings of singular curves over finite fields

Author

Yves Aubry, Marc Perret, Institut de mathématiques de Luminy (IML), Centre National de la Recherche Scientifique (CNRS)-Université de la Méditerranée - Aix-Marseille 2, École normale supérieure - Lyon (ENS Lyon), Université de la Méditerranée - Aix-Marseille 2-Centre National de la Recherche Scientifique (CNRS), and École normale supérieure de Lyon (ENS de Lyon)

Subjects
Discrete mathematics, Absolutely irreducible, General Mathematics, 010102 general mathematics, Local ring, 0102 computer and information sciences, Algebraic geometry, 16. Peace & justice, 01 natural sciences, Combinatorics, Character sum, Number theory, Finite field, 010201 computation theory & mathematics, Arithmetic genus, [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], 0101 mathematics, Algebraic number, Mathematics
Abstract

International audience; We prove that if $f : Y\longrightarrow X$ is a finite fiat morphism between two reduced absolutely irreducible algebraic projective curves defined over the finite field ${\sb F}_q$, then $$\mid \sharp Y({\sb F}_q) - \sharp X({\sb F}_q)\mid \leq 2({\pi}_Y - {\pi}_X)\sqrt q,$$ where $\pi_C$ is the arithmetic genus of a curve $C$. As application, we give some character sum estimation on singular curves.

Published
1995

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