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Linearized polynomials over finite fields

NettetKeywords: A ne equation Finite eld Zeros of a polynomial Linearized polynomial. Mathematics Subject Classi cation. 11D04, 12E05, 12E12. 1 Introduction Let F pn be the nite eld of pn elements where pis a prime and n 1 is a positive integer. A polynomial L(X) 2F pn[X] of shape L(X) = Xt i=0 a iX pi;a i 2F pn is called a linearized polynomial over ... 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 …

Permutation polynomials from a linearized decomposition

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 ... Nettet5. jan. 2024 · In this work, linearized multivariate skew polynomials over division rings are introduced. Such polynomials are right linear over the corresponding centralizer … gary brooker say it ain\u0027t so joe https://merklandhouse.com

[2012.15357] $r$-fat linearized polynomials over finite fields

Nettet1. mar. 2024 · We describe a method for constructing permutations of finite fields from the nilpotent linearized polynomials and, for some special permutations, we determine … Nettet1. jul. 2013 · Polynomials over F q n of the form (1) L ( x) = ∑ i = 0 t a i x q i, t ∈ N are often known as linearized polynomials. Such special kind of polynomials can induce linear transformations of F q n over F q. Considered as maps between finite fields, … NettetAccess to Project Euclid content from this IP address has been suspended. If your organization is a subscriber, please contact your librarian/institutional administrator. If you are a non-subscriber, please contact the Help Desk. Business Office. 905 W. Main Street. Suite 18B. Durham, NC 27701 USA. blacksmiths east sussex

Evaluation of weil sums for some polynomials and associated

Category:Nilpotent linearized polynomials over finite fields and …

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Linearized polynomials over finite fields

On the inverses of some classes of permutations of finite fields

Nettet27. apr. 2024 · Permutation polynomials from a linearized decomposition. Lucas Reis, Qiang Wang. In this paper we discuss the permutational property of polynomials of the form over the finite field , where are -linearized polynomials. The restriction implies a nice correspondence between the pair and the pair of conventional -associates over of … Nettet23. nov. 2012 · Linearized polynomials over finite fields revisited. We give new characterizations of the algebra formed by all linearized polynomials over the finite …

Linearized polynomials over finite fields

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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. jan. 2009 · finite field polynomial dynamics linearized polynomial period. Type Research Article. Information Proceedings of the Edinburgh Mathematical Society, …

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. Nettet1. 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

Nettet23. sep. 2024 · General conditions for linearized polynomials over $${{\mathbb {F}}}_{q^n}$$ to be scattered can be deduced from the recent results in Csajbók (Scalar q-subresultants and Dickson matrices, 2024), Csajbók et al. (Finite Fields Appl 56:109–130, 2024), McGuire and Sheekey (Finite Fields Appl 57:68–91, 2024), Polverino and Zullo … Nettet8. aug. 2024 · Then we present 2-to-1 polynomial mappings in classical classes of polynomials: linearized polynomials and monomials, low degree polynomials, …

Nettet5. jun. 2012 · Summary. The theory of polynomials over finite fields is important for investigating the algebraic structure of finite fields as well as for many applications. …

NettetIn mathematics, particularly computational algebra, Berlekamp's algorithm is a well-known method for factoring polynomials over finite fields (also known as Galois fields).The … blacksmith second seaNettet1. jul. 2024 · We completely determine the possible values of r when considering linearized polynomials over F q 4 and we also provide one family of 1-fat … blacksmith seattle waNettetA polynomial f over F q is called a permutation polynomial of F q if the polynomial f induces a one-one map on F q onto itself. Permutation polynomials have been a subject of study for almost one and a half century see [6], [7] and Chapter 7 of [8]. A polynomial L(x) ∈ F qm[x] is called a p- polynomial or linearized polynomial over F q if L(x ... blacksmith seattle forgegary brooker whiter shade of pale in denmarkNettet2. jun. 2024 · TL;DR The PhD thesis linked below mentions linearized polynomials, did not dig deep to figure out the details. See also the third reference where linearized polynomial permutations are discussed. As described on the Wikipedia page linked to in the comment by @kelalaka there are a number of families of permutation polynomials … gary brooker vocal rangeNettet8. 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 … blacksmiths edinburgh areaNettet15. mar. 2024 · We introduce the class of the linearized polynomials... Find, read and cite all the research you need on ResearchGate Article PDF Available Nilpotent linearized … blacksmith seed