TY - JOUR

T1 - Value sets of Dickson polynomials over finite fields

AU - Chou, Wun Seng

AU - Gomez-Calderon, Javier

AU - Mullen, Gary L.

N1 - Funding Information:
* This author would like to thank the National Security Agency for partial support under grant agreement No. MDA904-87-H-2023.

PY - 1988/11

Y1 - 1988/11

N2 - Let Fq denote the finite field of order q where q is a prime power. If a ∈ Fq and d ≥ 1 is an integer, define the Dickson polynomial gd(x, a) = ∑t=0[ d 2] ( d (d-t))(td-t)(-atxd-2t. Let {gd(x, a) | x ∈ Fq} denote the image or value set of the polynomial gd(x, a). In this paper we determine the cardinality of the value set for the Dickson polynomial gd(x, a) over the finite field Fq.

AB - Let Fq denote the finite field of order q where q is a prime power. If a ∈ Fq and d ≥ 1 is an integer, define the Dickson polynomial gd(x, a) = ∑t=0[ d 2] ( d (d-t))(td-t)(-atxd-2t. Let {gd(x, a) | x ∈ Fq} denote the image or value set of the polynomial gd(x, a). In this paper we determine the cardinality of the value set for the Dickson polynomial gd(x, a) over the finite field Fq.

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U2 - 10.1016/0022-314X(88)90006-6

DO - 10.1016/0022-314X(88)90006-6

M3 - Article

AN - SCOPUS:38249027569

VL - 30

SP - 334

EP - 344

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

IS - 3

ER -