Some results on permutation polynomials over finite fields |
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Authors: | Rex Matthews |
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Affiliation: | (1) School of Information Science and Technology, Flinders University, South Australia |
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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. |
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Keywords: | Permutation polynomials Finite fields |
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