Linearized polynomials over finite fields

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Nettet1. 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 … Nettet20. jan. 2009 · finite field polynomial dynamics linearized polynomial period. Type Research Article. Information Proceedings of the Edinburgh Mathematical Society, …

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Nettet2. 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 … NettetA 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 ... chevy volt electric motor specs

On Two-to-One Mappings Over Finite Fields - IEEE Xplore

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 … 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 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. Nettet8. aug. 2024 · Then we present 2-to-1 polynomial mappings in classical classes of polynomials: linearized polynomials and monomials, low degree polynomials, Dickson polynomials and Muller-Cohen-Matthews polynomials, etc. Lastly, we show applications of 2-to-1 mappings over finite fields for constructions of bent Boolean and vectorial … chevy volt fire hazard

On the c-differential uniformity of certain maps over finite fields ...

Nettet14. feb. 2024 · We study polynomials as quadratic forms over finite fields of odd characteristic. For these polynomials, we establish a connection between a kind of character sums, called Weil sums, and invariants of quadratic forms. A general method is presented to characterize quadratic forms based on coefficients of polynomials, which … Nettet2. nov. 2009 · Above all, irreducible polynomials—the prime elements of the polynomial ring over a finite field—are indispensable for constructing finite fields and computing … chevy volt fast chargingNettet8. aug. 2001 · In this paper we study linearized permutation polynomials under finite field extensions and curves of the form where a0an−1 ≠0. Firstly, we find such … chevy volt finance deals

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Linearized polynomials over finite fields

A condition for scattered linearized polynomials involving Dickson ...

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 … 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 ...

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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, … 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.

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 … Nettet14. mar. 2024 · Again, by the theory of linearized and conventional associates this implies that $$ L(x)\mid x^{2^{127}}-x. $$ Namely, if a polynomial divides another, then its linearized associate divides the linearized associate of the other even symbolically (= as an innermost composition factor), and hence also in the polynomial ring.

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 … Nettet18. jul. 2024 · I'm Ehsan Hosseini, Applied Mathematics graduate from Yazd University, majoring in Numerical Analysis and now I am Teacher …

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. …

Nettet13. aug. 2024 · Comparing the construction methods of MUBs in this paper with other methods in the existing literature, our construction methods are mainly reflected in three aspects: (1) We proposed three new construction methods which are different from other methods, one uses p-ary weakly regular bent functions, the other uses permutation … goodwill store asheboro ncNettetProperties. The map x ↦ L(x) is a linear map over any field containing F q.; The set of roots of L is an F q-vector space and is closed under the q-Frobenius map.; … goodwill store ashland oregonNettet2. nov. 2009 · Above all, irreducible polynomials—the prime elements of the polynomial ring over a finite field—are indispensable for constructing finite fields and computing with the elements of a finite field. ... Linearized polynomials are singled out by the property that all the exponents occurring in them are powers of the characteristic. goodwill store ashland kyNettet26. 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. goodwill store ashland wiNettet27. 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 … chevy volt forumNettet1. 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 … chevy volt for saleNettet23. 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 … chevy volt first year