Scalar Polynomial Functions on the NxN Matrices over a Finite Field.
CLEMSON UNIV S C DEPT OF MATHEMATICAL SCIENCES
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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 fx with coefficients in a finite field F in order that it defines via substitution a one-one onto function a permutation from Fnxn, the nxn matrices over F, to Fnxn.
- Theoretical Mathematics