Construction of Permutation Polynomials of Certain Specific Cycle Structure over Finite Fields

Abstract

For a finite field of odd number of elements we construct families of permutation binomials and permutation trinomials with one fixed-point (namely zero) and remaining elements being permuted as disjoint cycles of same length. Binomials and trinomials providing permutations with cycles of many lengths with certain frequency are also constructed.

arXiv comment10 pages, 1 table, Comments welcome