Results 21 to 30 of about 127,631 (176)
Mathematics, 2023 The factorization of groups into a Zappa–Szép product, or more generally into a k-fold Zappa–Szép product of its subgroups, is an interesting problem, since it eases the multiplication of two elements in a group and has recently been applied to public ...
Robert Shwartz, Hadas Yadayi
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On some permutation polynomials over finite fields
International Journal of Mathematics and Mathematical Sciences, 2005 Let p be prime, q=pm, and q−1=7s. We completely describe the permutation behavior of the binomial P(x)=xr(1+xes) (1≤e≤6) over a finite field Fq in terms of the sequence {an} defined by the recurrence relation an=an−1+2an−2−an−3 (n≥3) with initial ...
Amir Akbary, Qiang Wang
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Lower Bound of the Complexity of Seven-Valued Functions in the Class of Polarized Polynomials
Известия Иркутского государственного университета: Серия "Математика", 2017 One of the directions of the investigation of functions over finite fields is the study of their representations, including polynomial ones. In the area of polynomial representations of functions the problem of estimating the complexity of such ...
A.S. Baliuk, A.S. Zinchenko
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Factoring Polynomials over Finite Fields using Balance Test [PDF]
, 2008 We study the problem of factoring univariate polynomials over finite fields. Under the assumption of the Extended Riemann Hypothesis (ERH), (Gao, 2001) designed a polynomial time algorithm that fails to factor only if the input polynomial satisfies a ...
Saha, Chandan
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Lietuvos Matematikos Rinkinys, 2004 In the paper the Pell conics method for factoring integers, based on observations of Lemmermeyer [2, 3], is presented explicitly. Moreover, a similar algorithm for factoring polynomials over finite fields is given.
Rasa Šleževičienė
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On the Structure of Valiant's Complexity Classes [PDF]
Discrete Mathematics & Theoretical Computer Science, 1999 In Valiant developed an algebraic analogue of the theory of NP-completeness for computations of polynomials over a field. We further develop this theory in the spirit of structural complexity and obtain analogues of well-known results by Baker, Gill, and
Peter Bürgisser
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Value sets of bivariate folding polynomials over finite fields [PDF]
, 2017 We find the cardinality of the value sets of polynomial maps associated with simple complex Lie algebras $B_2$ and $G_2$ over finite fields. We achieve this by using a characterization of their fixed points in terms of sums of roots of unity.Comment: 16 ...
Küçüksakallı, Ömer
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On polynomial factorization over finite fields [PDF]
Mathematics of Computation, 1981 Let f ( x ) f(x) be a polynomial over a finite field F. An algorithm for determining the degrees of the factors of f ( x ) f(x) is presented. As in the Berlekamp algorithm (1968) for determining the factors of f ( x )
Gunji, Hiroshi, Arnon, Dennis
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Faster Polynomial Multiplication over Finite Fields [PDF]
Journal of the ACM, 2017 Polynomials over finite fields play a central role in algorithms for cryptography, error correcting codes, and computer algebra. The complexity of multiplying such polynomials is still a major open problem. Let p be a prime, and let M p ( n )
Harvey, David +2 more
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Deterministic Construction of Compressed Sensing Matrices via Vector Spaces Over Finite Fields
IEEE Access, 2020 Compressed Sensing (CS) is a new signal processing theory under the condition that the signal is sparse or compressible. One of the central problems in compressed sensing is the construction of sensing matrices.
Xuemei Liu, Lihua Jia
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