Abstract
This paper deals with two questions concerning permutation polynomials in several variables. Lidl and Niederreiter have considered the problem of when a sum of permutation polynomials in disjoint sets of variables is itself a permutation polynomial, and in the case of prime fields have shown that it is necessary and sufficient that at least one summand be a permutation polynomial. They also showed that in the case of non-prime fields this condition is not necessary. In this paper, a necessary and sufficient condition is obtained for the general case which specialises to the previous result for prime fields. The second part extends a criterion of Niederreiter for permutation polynomials over prime fields to any finite field.
Article PDF
Similar content being viewed by others
References
Lidl, R., Niederreiter, H.: On orthogonal systems and permutation polynomials in several variables. Acta Arith.22, 257–265 (1973)
Lidl, R., Niederreiter, H.: Finite fields. Reading, MA: Addison-Wesley 1983
McDonald, B.: Finite rings with identity. New York: Dekker, 1974
Niederreiter, H.: Permutation polynomials in several variables. Acta Sci. Math. Szeged33, 53–58 (1972)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Matthews, R. Some results on permutation polynomials over finite fields. AAECC 3, 63–65 (1992). https://doi.org/10.1007/BF01189024
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01189024