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
SN - 0022-314X
VL - 30
SP - 334
EP - 344
JO - Journal of Number Theory
JF - Journal of Number Theory
IS - 3
ER -