The Number of Polynomial Functions Which Permute the Matrices over a Finite Field,
Abstract
Let F denote a finite field and let f sub (n x n) denote the n x n matrices over F. A function f:F sub (n x n) maps to F sub (n x n) is called a (scalar) polynomial function on F sub (n x n) if and only if there exists a polynomial f(x) an element of F(in brackets:(x)) which represents f under substitution. A formula is obtained for the number of polynomial function on F sub (n x n) which are permutations of F sub (n x n). In the process a procedure is outlined for obtaining a unique polynomial representations of each permutation polynomial function on F sub (n x n).
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 30, 1974
- Accession Number
- ADA009813
Entities
People
- Joel V. Brawley Jr.
Organizations
- Clemson University