Permutation polynomials of degree 6 or 7 over finite fields of characteristic 2
نویسندگان
چکیده
Article history: Received 12 February 2010 Accepted 18 July 2010 Available online xxxx Communicated by Rudolf Lidl
منابع مشابه
Enumerating Permutation Polynomials over Finite Fields by Degree
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...
متن کاملPermutation Polynomials and Resolution of Singularities over Finite Fields
A geometric approach is introduced to study permutation polynomials over a finite field. As an application, we prove that there are no permutation polynomials of degree 2/ over a large finite field, where / is an odd prime. This proves that the Carlitz conjecture is true for n = 21. Previously, the conjecture was known to be true only for n < 16.
متن کاملNew Constructions of Permutation Polynomials of the Form $x^rh\left(x^{q-1}\right)$ over $\mathbb{F}_{q^2}$
Permutation polynomials over finite fields have been studied extensively recently due to their wide applications in cryptography, coding theory, communication theory, among others. Recently, several authors have studied permutation trinomials of the form xh ( x ) over Fq2 , where q = 2 , h(x) = 1+x+x and r, s, t, k > 0 are integers. Their methods are essentially usage of a multiplicative versio...
متن کاملNew Permutation Trinomials From Niho Exponents over Finite Fields with Even Characteristic
In this paper, a class of permutation trinomials of Niho type over finite fields with even characteristic is further investigated. New permutation trinomials from Niho exponents are obtained from linear fractional polynomials over finite fields, and it is shown that the presented results are the generalizations of some earlier works.
متن کاملNew Permutation Trinomials Constructed from Fractional Polynomials
Permutation trinomials over finite fields consititute an active research due to their simple algebraic form, additional extraordinary properties and their wide applications in many areas of science and engineering. In the present paper, six new classes of permutation trinomials over finite fields of even characteristic are constructed from six fractional polynomials. Further, three classes of p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Finite Fields and Their Applications
دوره 16 شماره
صفحات -
تاریخ انتشار 2010