17,353 research outputs found
A Recursive Construction of Permutation Polynomials over with Odd Characteristic from R\'{e}dei Functions
In this paper, we construct two classes of permutation polynomials over
with odd characteristic from rational R\'{e}dei functions. A
complete characterization of their compositional inverses is also given. These
permutation polynomials can be generated recursively. As a consequence, we can
generate recursively permutation polynomials with arbitrary number of terms.
More importantly, the conditions of these polynomials being permutations are
very easy to characterize. For wide applications in practice, several classes
of permutation binomials and trinomials are given. With the help of a computer,
we find that the number of permutation polynomials of these types is very
large
Permutation polynomials induced from permutations of subfields, and some complete sets of mutually orthogonal latin squares
We present a general technique for obtaining permutation polynomials over a
finite field from permutations of a subfield. By applying this technique to the
simplest classes of permutation polynomials on the subfield, we obtain several
new families of permutation polynomials. Some of these have the additional
property that both f(x) and f(x)+x induce permutations of the field, which has
combinatorial consequences. We use some of our permutation polynomials to
exhibit complete sets of mutually orthogonal latin squares. In addition, we
solve the open problem from a recent paper by Wu and Lin, and we give simpler
proofs of much more general versions of the results in two other recent papers.Comment: 13 pages; many new result
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