On Inverses of Permutation Polynomials of Small Degree Over Finite Fields
نویسندگان
چکیده
منابع مشابه
Enumerating permutation polynomials over finite fields by degree II
This note is a continuation of a paper by the same authors that appeared in 2002 in the same journal. First we extend the method of the previous paper proving an asymptotic formula for the number of permutations for which the associated permutation polynomial has d coefficients in specified fixed positions equal to 0. This also applies to the function Nq,d that counts the number of permutations...
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fσ has the property that fσ(a) = σ(a) for every a ∈ Fq and this explains its name. For an account of the basic properties of permutation polynomials we refer to the book of Lidl and Niederreiter [5]. From the definition, it follows that for every σ ∂(fσ) ≤ q − 2. A variety of problems and questions regarding Permutation polynomials have been posed by Lidl and Mullen in [3, 4]. Among these there...
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Let Fq be a finite field of q = pm elements with characteristic p. A polynomial P(x) ∈ Fq[x] is called a permutation polynomial of Fq if P(x) induces a bijective map from Fq to itself. In general, finding classes of permutation polynomials of Fq is a difficult problem (see [3, Chapter 7] for a survey of some known classes). An important class of permutation polynomials consists of permutation p...
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In this paper, we construct a new class of complete permutation monomials and several classes of permutation polynomials. Further, by giving another characterization of opolynomials, we obtain a class of permutation polynomials of the form G(x) + γTr(H(x)), where G(X) is neither a permutation nor a linearized polynomial. This is an answer to the open problem 1 of Charpin and Kyureghyan in [P. C...
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We present new classes of permutation polynomials over finite fields. If q is the order of a finite field, some polynomials are of form xrf(x(q−1)/d), where d|(q − 1). Other permutation polynomials are related with the trace function. 2000 Mathematics Subject Classification: Primary 11T06.
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2020
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2019.2939113