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CORR
2006
Springer
163views Education» more  CORR 2006»
13 years 8 months ago
Finding roots of polynomials over finite fields
In this paper we propose an improved algorithm for finding roots of polynomials over finite fields. This makes possible significant speed up of the decoding process of BCH, Reed-S...
Sergei V. Fedorenko, Peter Vladimirovich Trifonov
FOCM
2008
76views more  FOCM 2008»
13 years 8 months ago
On Smale's 17th Problem: A Probabilistic Positive Solution
Smale's 17th Problem asks "Can a zero of n complex polynomial equations in n unknowns be found approximately, on the average [for a suitable probability measure on the s...
Carlos Beltrán, Luis Miguel Pardo
ISSAC
2004
Springer
106views Mathematics» more  ISSAC 2004»
14 years 1 months ago
Factoring polynomials via polytopes
We introduce a new approach to multivariate polynomial factorisation which incorporates ideas from polyhedral geometry, and generalises Hensel lifting. Our main contribution is to...
Fatima Abu Salem, Shuhong Gao, Alan G. B. Lauder
SODA
2008
ACM
75views Algorithms» more  SODA 2008»
13 years 10 months ago
Strongly polynomial and fully combinatorial algorithms for bisubmodular function minimization
Bisubmodular functions are a natural "directed", or "signed", extension of submodular functions with several applications. Recently Fujishige and Iwata showed ...
S. Thomas McCormick, Satoru Fujishige
CORR
2008
Springer
132views Education» more  CORR 2008»
13 years 8 months ago
Trading GRH for algebra: algorithms for factoring polynomials and related structures
Abstract. In this paper we develop a general technique to eliminate the assumption of the Generalized Riemann Hypothesis (GRH) from various deterministic polynomial factoring algor...
Gábor Ivanyos, Marek Karpinski, Lajos R&oac...