کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4583052 1333877 2012 30 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A new approach to permutation polynomials over finite fields
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
A new approach to permutation polynomials over finite fields
چکیده انگلیسی

Let p be a prime and q=pκ. We study the permutation properties of the polynomial gn,q∈Fp[x] defined by the functional equation ∑a∈Fq(x+a)n=gn,q(xq−x). The polynomial gn,q is a q-ary version of the reversed Dickson polynomial in characteristic 2. We are interested in the parameters (n,e;q) for which gn,q is a permutation polynomial (PP) of Fqe. We find several families of such parameters and obtain various necessary conditions on such parameters. Initial results, both theoretical and numerical, indicate that the class gn,q contains an abundance of PPs over finite fields, many of which are yet to be explained and understood.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Finite Fields and Their Applications - Volume 18, Issue 3, May 2012, Pages 492-521