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» Permutations, hyperplanes and polynomials over finite fields
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JCT
2008
67views more  JCT 2008»
15 years 4 months ago
On the number of directions determined by a pair of functions over a prime field
A three-dimensional analogue of the classical direction problem is proposed and an asymptotically sharp bound for the number of directions determined by a nonplanar set in AG(3, p)...
Simeon Ball, András Gács, Pét...
MOC
1998
97views more  MOC 1998»
15 years 3 months ago
Euclid's algorithm and the Lanczos method over finite fields
Abstract. This paper shows that there is a close relationship between the Euclidean algorithm for polynomials and the Lanczos method for solving sparse linear systems, especially w...
Jeremy Teitelbaum
FOCM
2008
77views more  FOCM 2008»
15 years 4 months ago
Modular Counting of Rational Points over Finite Fields
Let Fq be the finite field of q elements, where q = ph. Let f(x) be a polynomial over Fq in n variables with m non-zero terms. Let N(f) denote the number of solutions of f(x) = 0 ...
Daqing Wan
ISSAC
2009
Springer
163views Mathematics» more  ISSAC 2009»
15 years 10 months ago
Fast arithmetics in artin-schreier towers over finite fields
An Artin-Schreier tower over the finite field Fp is a tower of field extensions generated by polynomials of the form Xp − X − α. Following Cantor and Couveignes, we give a...
Luca De Feo, Éric Schost
AAECC
1997
Springer
115views Algorithms» more  AAECC 1997»
15 years 8 months ago
Efficient Multivariate Factorization over Finite Fields
We describe the Maple [23] implementation of multivariate factorization over general finite fields. Our first implementation is available in Maple V Release 3. We give selected det...
Laurent Bernardin, Michael B. Monagan