Factoring polynomials over finite fields
Factoring Polynomials over Finite Fields
... The Problem The Well-Known Methods The Main Idea Singular Hyperelliptic Curves Factoring f (x ). Factoring Polynomials over Finite Fields Enver Ozdemir[r] ...
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Factoring Polynomials Over Finite Fields: A Survey
... polynomial over a finite field is of interest not only inde- pendently but also for many applications in computer algebra, algebraic coding theory, cryptography, and computational number ...factorization ...
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Factoring polynomials over finite fields
... Let p an odd prime and let F p = Z/pZ the (unique up to automorphism) field with p-elements. We want to classify finite fields up to automorphism. Question 1 Give a field with 4 elements. Is there any field ...
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Factoring Multivariate Polynomials over Finite Fields
... of factoring polynomials over finite fields has also made partial ...multivariate polynomials over finite ...partially factoring multivariate ...
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Factoring polynomials over special finite fields version
... i=0 R/I i is an isomorphism. Using linear algebra over F p one determines which of the elements α n/r − ζ in/r are non-units or, equivalently, which of the rings R/I i are non-zero. This occurs for at least one of ...
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Factoring Polynomials
... Factoring Polynomials Sue Geller ∗ June 19, 2006 Factoring polynomials over the rational numbers, real numbers, and com- plex numbers has long been a standard topic of high school ...
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Factoring Dickson polynomials over finite fields
... irreducible over F q ; hence the stated factorization is ...a) over F q ...irreducible polynomials in F q [X], which occur in cliques corresponding to the divisors d of ...
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SUBQUADRATIC-TIME FACTORING OF POLYNOMIALS OVER FINITE FIELDS
... It is also possible to obtain a practical version of the Fast Black Box Berlekamp algorithm using similar techniques, although we have not as yet implemented this. That algorithm would require significantly fewer GCD ...
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Factoring and Testing Irreducibility of Sparse Polynomials over Small Finite Fields
... is over F p ; the algorithm works over Z and reduces mod p in the ...evaluation over Z is done by CRT modulo a bunch of smaller primes, and so ...
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Factoring polynomials over p-adic fields
... We will factor polynomials over a finite algebraic extension K of Q p . See Chapter 5 of [14] for properties of these extensions. Let π be a uniformizer of K. In the case when K is an unramified ...
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Factoring polynomials over Z4 and over certain Galois rings
... Theory, 40:301–319, 1994. [9] B. R. McDonald. Finite Rings with Identity. Marcel Dekker, New York, 1974. [10] S. Pauli. Factoring polynomials over local fields. J. Symb. Comput., ...
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On permutation polynomials over finite fields
... consider the problem of characterizing permutation polynomials; that is, we seek conditions on the coefficients of a polynomial which are necessary and sufficient for it to represent a p[r] ...
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A Lecture on the Complexity of Factoring Polynomials over Global Fields
... for factoring polynomials over global fields with their complexity analysis from our experiments on the ...of factoring parametric multivariate polynomials that is used for solving ...
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On some permutation polynomials over finite fields
... Amir Akbary: Department of Mathematics and Computer Science, University of Lethbridge, 4401 University Drive West, Lethbridge, AB, Canada T1K 3M4. E-mail address : [email protected][r] ...
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Finding irreducible polynomials over finite fields
... fouiid in polvnomiil linic b^ niivc snrdi Ί(ιρ (ΐ\ is n«w ( tsil) si cn to bi rompiitiblc in.. pol>iH)iiuil tmR llif[r] ...
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Codes from Polynomials over Finite Fields
... University of California, Irvine Colorado State Colloquium.. February 8, 2021.[r] ...
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Factorization Algorithms for Polynomials over Finite Fields
... polynomial over a field can be expressed as a product of ir- reducible ...of polynomials over finite fields has great importance in coding ...mials over finite ...
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Several Classes of Permutation Polynomials over Finite Fields
... [1] Hermite, Ch. (1863) Sur les Fonctions de Sept Lettres. C.R. Acad. Sci. Paris, 57, 750-757. [2] Dickson, L.E. (1896) The Analytic Representation of Substitutions on a power of a Prime Number of Letters with a ...
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P schemes and Deterministic Polynomial Factoring Over Finite Fields
... H = Gal(L/K) ←→ K = L H , where L H denotes the fixed field of H . In Chapter 3, we design a generic algorithm, which we refer to as the P -scheme algorithm , that deterministically factorizes f under GRH given f and f ˜ ...
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Efficient Indexing of Necklaces and Irreducible Polynomials over Finite Fields
... n over alphabet Σ. A read-once branching program of length n over alphabet Σ is an acyclic directed graph with vertex layers numbered from 0 to n, where (1) layer 0 has a single start node, (2) there is a ...
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