Accession Number : AD0766154

Title :   Scalar Polynomial Functions on the NxN Matrices over a Finite Field.

Descriptive Note : Technical rept.,

Corporate Author : CLEMSON UNIV S C DEPT OF MATHEMATICAL SCIENCES

Personal Author(s) : Brawley,J. V. ; Carlitz,L. ; Levine,Jack

Report Date : 24 JUL 1973

Pagination or Media Count : 35

Abstract : The use of the theory of finite fields in areas of discrete linear modeling such as coding theory, finite linear sequential machines, algebraic cryptography and the construction of block designs is well-known. Many times one has the task of constructing (based on a finite field) a function having certain prescribed properties. Of such a nature is the material contained in the report. In particular, the authors determined among other things, necessary and sufficient conditions on a polynomial f(x) with coefficients in a finite field F in order that it defines via substitution a one-one onto function (a permutation) from F(nxn), the nxn matrices over F, to F(nxn).

Descriptors :   (*MATRICES(MATHEMATICS), TRANSFORMATIONS(MATHEMATICS)), POLYNOMIALS, PERMUTATIONS, CODING, CRYPTOGRAPHY, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE