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FFA
2010
84views more  FFA 2010»
13 years 5 months ago
Generating series for irreducible polynomials over finite fields
We count the number of irreducible polynomials in several variables of a given degree over a finite field. The results are expressed in terms of a generating series, an exact for...
Arnaud Bodin
FFA
2008
75views more  FFA 2008»
13 years 7 months ago
Syntactical and automatic properties of sets of polynomials over finite fields
Syntactical properties of representations of integers in various number systems are well-known and have been extensively studied. In this paper, we transpose the notion of recogniz...
Michel Rigo
CAP
2010
13 years 2 months ago
Parallel sparse polynomial interpolation over finite fields
We present a probabilistic algorithm to interpolate a sparse multivariate polynomial over a finite field, represented with a black box. Our algorithm modifies the algorithm of Ben...
Seyed Mohammad Mahdi Javadi, Michael B. Monagan
ECCC
2010
104views more  ECCC 2010»
13 years 7 months ago
Pseudorandom generators for CC0[p] and the Fourier spectrum of low-degree polynomials over finite fields
In this paper we give the first construction of a pseudorandom generator, with seed length O(log n), for CC0[p], the class of constant-depth circuits with unbounded fan-in MODp ga...
Shachar Lovett, Partha Mukhopadhyay, Amir Shpilka
CSR
2006
Springer
13 years 11 months ago
Complexity of Polynomial Multiplication over Finite Fields
Let Mq (n ) denote the number of multiplications required to compute the coefficients of the product of two polynomials of degree n over a q -element field by means of bilinear alg...
Michael Kaminski