Dickson Polynomials Over Finite Fields and Complete Mappings
Canadian mathematical bulletin, Tome 30 (1987) no. 1, pp. 19-27
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Dickson polynomials over finite fields are familiar examples of permutation polynomials, i.e. of polynomials for which the corresponding polynomial mapping is a permutation of the finite field. We prove that a Dickson polynomial can be a complete mapping polynomial only in some special cases. Complete mapping polynomials are of interest in combinatorics and are defined as polynomials f(x) over a finite field for which both f(x) and f(x) + x are permutation polynomials. Our result also verifies a special case of a conjecture of Chowla and Zassenhaus on permutation polynomials.
Mullen, Gary L.; Niederreiter, Harald. Dickson Polynomials Over Finite Fields and Complete Mappings. Canadian mathematical bulletin, Tome 30 (1987) no. 1, pp. 19-27. doi: 10.4153/CMB-1987-003-3
@article{10_4153_CMB_1987_003_3,
author = {Mullen, Gary L. and Niederreiter, Harald},
title = {Dickson {Polynomials} {Over} {Finite} {Fields} and {Complete} {Mappings}},
journal = {Canadian mathematical bulletin},
pages = {19--27},
year = {1987},
volume = {30},
number = {1},
doi = {10.4153/CMB-1987-003-3},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1987-003-3/}
}
TY - JOUR AU - Mullen, Gary L. AU - Niederreiter, Harald TI - Dickson Polynomials Over Finite Fields and Complete Mappings JO - Canadian mathematical bulletin PY - 1987 SP - 19 EP - 27 VL - 30 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1987-003-3/ DO - 10.4153/CMB-1987-003-3 ID - 10_4153_CMB_1987_003_3 ER -
%0 Journal Article %A Mullen, Gary L. %A Niederreiter, Harald %T Dickson Polynomials Over Finite Fields and Complete Mappings %J Canadian mathematical bulletin %D 1987 %P 19-27 %V 30 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1987-003-3/ %R 10.4153/CMB-1987-003-3 %F 10_4153_CMB_1987_003_3
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