Equations in Finite Fields
نویسندگان
چکیده
منابع مشابه
Discrete Integrable Equations over Finite Fields
Discrete integrable equations over finite fields are investigated. The indeterminacy of the equation is resolved by treating it over a field of rational functions instead of the finite field itself. The main discussion concerns a generalized discrete KdV equation related to a Yang–Baxter map. Explicit forms of soliton solutions and their periods over finite fields are obtained. Relation to the ...
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Ahstruct-A “coordinate recurrence” method for solving sparse systems of linear equations over finite fields is described. The algorithms discussed all require O( n,( w + nl) logkn,) field operations, where nI is the maximum dimension of the coefficient matrix, w is approximately the number of field operations required to apply the matrix to a test vector, and the value of k depends on the algor...
متن کاملOn the Solvability of Bilinear Equations in Finite Fields
We consider the equation ab+ cd = λ, a ∈ A, b ∈ B, c ∈ C, d ∈ D, over a finite field q of q elements, with variables from arbitrary sets A,B, C,D ⊆ q. The question of solvability of such and more general equations has recently been considered by Hart and Iosevich, who, in particular, prove that if #A#B#C#D ≥ Cq, for some absolute constant C > 0, then above equation has a solution for any λ ∈ q....
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We present a polynomial-time algorithm for computing the zeta function of a smooth projective hypersurface of degree d over a finite field of characteristic p, under the assumption that p is a suitably small odd prime and does not divide d. This improves significantly upon an earlier algorithm of the author and Wan which is only polynomial-time when the dimension is fixed.
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1954
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.40.11.1072