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On the Primitivity of Trinomials over Small Finite Fields
"... Abstract: In this paper, we explore the primitivity of trinomials over small finite fields. We extend the results of the primitivity of trinomials xn + ax + b over F4 [1] to the general form xn + axk + b. We prove that for given n and k, one of all the trinomials xn + axk + b with b being the primit ..."
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Abstract: In this paper, we explore the primitivity of trinomials over small finite fields. We extend the results of the primitivity of trinomials xn + ax + b over F4 [1] to the general form xn + axk + b. We prove that for given n and k, one of all the trinomials xn + axk + b with b being
A Deterministic Multivariate Interpolation Algorithm for Small Finite Fields
, 2002
"... We present a new multivariate interpolation algorithm over arbitrary fields which is primarily suited for small finite fields. Given function values at arbitrary t points, we show that it is possible to find an nvariable interpolating polynomial with at most t terms, using the number of field oper ..."
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Cited by 4 (1 self)
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We present a new multivariate interpolation algorithm over arbitrary fields which is primarily suited for small finite fields. Given function values at arbitrary t points, we show that it is possible to find an nvariable interpolating polynomial with at most t terms, using the number of field
Simultaneous Modular Reduction and Kronecker Substitution for Small Finite Fields ∗
, 2008
"... We present algorithms to perform modular polynomial multiplication or modular dot product efficiently in a single machine word. We pack polynomials into integers and perform several modular operations with machine integer or floating point arithmetic. The modular polynomials are converted into integ ..."
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Cited by 7 (1 self)
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efficient ways to recover the modular values of the coefficients. This leads to practical gains of quite large constant factors for polynomial multiplication, prime field linear algebra and small extension field arithmetic. 1
CURVES OF GENUS 3 OVER SMALL FINITE FIELDS JAAP TOP
, 2003
"... The maximal number of rational points that a (smooth, geometrically irreducible) curve of genus g over a finite field Fq of cardinality q can have, is denoted by Nq(g). The interest in this number, particularly for fixed q as a function in g, arose primarily during the last two decades ..."
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The maximal number of rational points that a (smooth, geometrically irreducible) curve of genus g over a finite field Fq of cardinality q can have, is denoted by Nq(g). The interest in this number, particularly for fixed q as a function in g, arose primarily during the last two decades
Computing irreducible representations of supersolvable groups over small finite fields
 Mathematics of Computation, Volume 66, Number 218
, 1997
"... Abstract. We present an algorithm to compute a full set of irreducible representations of a supersolvable group G over a finite field K, charK ∤ G, which is not assumed to be a splitting field of G. The main subroutines of our algorithm are a modification of the algorithm of Baum and Clausen (Math ..."
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Abstract. We present an algorithm to compute a full set of irreducible representations of a supersolvable group G over a finite field K, charK ∤ G, which is not assumed to be a splitting field of G. The main subroutines of our algorithm are a modification of the algorithm of Baum and Clausen
Almost Primality of Group Orders of Elliptic Curves Defined over Small Finite Fields
"... Let E be an elliptic curve defined over a small finite field Fq / and 1. Introduction et p be a prime number. We give a conjectural formula for the 2. Probability of Primality probability that the order of the quotient group EflFqP)/E(IFq) is 3. Heuristics prime, and compare it with experimental da ..."
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Let E be an elliptic curve defined over a small finite field Fq / and 1. Introduction et p be a prime number. We give a conjectural formula for the 2. Probability of Primality probability that the order of the quotient group EflFqP)/E(IFq) is 3. Heuristics prime, and compare it with experimental
Factoring polynomials with rational coefficients
 MATH. ANN
, 1982
"... In this paper we present a polynomialtime algorithm to solve the following problem: given a nonzero polynomial fe Q[X] in one variable with rational coefficients, find the decomposition of f into irreducible factors in Q[X]. It is well known that this is equivalent to factoring primitive polynomia ..."
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Cited by 982 (11 self)
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for factoring polynomials over small finite fields, combined with Hensel's lemma. Next we look for the irreducible factor h o of f in
Results 1  10
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3,055,654