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
[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