Linearized polynomials over finite fields
NettetPermutation polynomials have been a subject of study for a long time and have applications in many areas of science and engineering. However, only a small number of specific classes of permutation polynomials are described in the literature so far. In this paper we present a number of permutation trinomials over finite fields, which are of … Nettet30. okt. 2013 · The study of computing compositional inverses of permutation polynomials over finite fields efficiently is motivated by an open problem proposed by G. L. Mullen (1991), as well as the potential ...
Linearized polynomials over finite fields
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Nettet18. jul. 2024 · I'm Ehsan Hosseini, Applied Mathematics graduate from Yazd University, majoring in Numerical Analysis and now I am Teacher … Nettet20. mar. 2014 · If we have GF(4) as an extension field, we can define a permutation polynomial of GF(4) like L(x), a linearized polynomial, of the followinf form: L(x)= \sum_{s=0}^{\r-1} a_s x^(q^r)e Is it possible to get more details for ... For multiplications over a finite field, what happens to the elements which, after modulo the reducing ...
Nettet31. okt. 2013 · We study the compositional inverses of some general classes of permutation polynomials over finite fields. We show that we can write these inverses in terms of the inverses of two other polynomials bijecting subspaces of the finite field, where one of these is a linearized polynomial. In some cases we are able to explicitly … Nettet26. mai 2024 · Finally we construct a linear MSRD code over an arbitrary finite field ${\bf F} ... This work considers the construction and decoding of folded linearized Reed-Solomon (FLRS) codes, ... A Skew Polynomial Framework. Alessandro Neri; Computer Science. Journal of Algebra. 2024; 14. PDF.
Nettet5. jan. 2024 · In this work, linearized multivariate skew polynomials over division rings are introduced. Such polynomials are right linear over the corresponding centralizer and generalize linearized polynomial rings over finite fields, group rings or differential polynomial rings. Their natural evaluation is connected to the remainder-based … Nettet1. feb. 2014 · However, over the finite field F q automorphisms defined by linearized polynomials have (in general) an entirely different structure. Namely, we will show that …
Nettet20. apr. 2024 · On the c-differential uniformity of certain maps over finite fields. We give some classes of power maps with low -differential uniformity over finite fields of odd characteristic, {for }. Moreover, we give a necessary and sufficient condition for a linearized polynomial to be a perfect -nonlinear function and investigate conditions …
NettetR-Fat Linearized Polynomials Over Finite Fields. 2024 • Ferdinando Zullo. Download Free PDF View PDF. ArXiv. Multi-Sidon spaces over finite fields. 2024 • Ferdinando Zullo. Download Free PDF View PDF. Advances in Mathematics of Communications. Two pointsets in $ \mathrm{PG}(2,q^n) $ and the associated codes. bob jenson air conditioning \u0026 heatingNettetAccess to Project Euclid content from this IP address has been suspended. If your organization is a subscriber, please contact your librarian/institutional administrator. If … bob jennings cincinnatiNettet1. mar. 2024 · We describe a method for constructing permutations of finite fields from the nilpotent linearized polynomials and, for some special permutations, we determine the cycle decomposition and the compositional inverse map. We present two further problems motivated by theoretical considerations. Problem 4.1 clipart of handshakeNettet8. nov. 2024 · We give some classes of power maps with low c-differential uniformity over finite fields of odd characteristic, for \(c=-1\).Moreover, we give a necessary and sufficient condition for a linearized polynomial to be a perfect c-nonlinear function and investigate conditions when perturbations of perfect c-nonlinear (or not) function via an arbitrary … bob jessee johnson city tnNettet1. feb. 2014 · However, over the finite field F q automorphisms defined by linearized polynomials have (in general) an entirely different structure. Namely, we will show that the linearized polynomial maps over F q are in one-to-one correspondence with matrices having coefficients in a univariate polynomial ring over F q. bob jenson air conditioning inc san diegoNettetThe problem of obtaining an optimal spline with free knots is tantamount to minimizing derivatives of a nonlinear differentiable function over a Banach space on a compact set. While the problem of data interpolation by quadratic splines has been accomplished, interpolation by splines of higher orders is far more challenging. In this paper, to … clip art of hands givingNettet1. sep. 2011 · A polynomial f ∈ F q [x] is called a permutation polynomial (PP) of F q it induces a one-to-one map from F q to itself. Permutation polynomials over finite fields have been an interesting subject of study for many ars, and have applications in coding theory [2], cryptography [7,6], combinatorial design theory [1], d other areas of … clipart of hands clapping