Specific permutation polynomials over finite fields
نویسنده
چکیده
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.
منابع مشابه
New classes of permutation binomials and permutation trinomials over finite fields
Permutation polynomials over finite fields play important roles in finite fields theory. They also have wide applications in many areas of science and engineering such as coding theory, cryptography, combinational design, communication theory and so on. Permutation binomials and trinomials attract people’s interest due to their simple algebraic form and additional extraordinary properties. In t...
متن کاملReversed Dickson polynomials over finite fields
Reversed Dickson polynomials over finite fields are obtained from Dickson polynomials Dn(x, a) over finite fields by reversing the roles of the indeterminate x and the parameter a. We study reversed Dickson polynomials with emphasis on their permutational properties over finite fields. We show that reversed Dickson permutation polynomials (RDPPs) are closely related to almost perfect nonlinear ...
متن کاملSeveral Classes of Permutation Polynomials over Finite Fields
Several classes of permutation polynomials of the form ( ) ( ) k p t x x + δ + L x − over finite fields are presented in this paper, which is a further investigation on a recent work of Li et al.
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 کاملOn the inverses of some classes of permutations of finite fields
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 obtain these inverses, thus obtaining the compositional inverse of the ...
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 17 شماره
صفحات -
تاریخ انتشار 2011