Dickson polynomials, completely normal polynomials and the cyclic module structure of specific extensions of finite fields

1996 ◽  
Vol 9 (2) ◽  
pp. 193-202 ◽  
Author(s):  
Alfred Scheerhorn
Keyword(s):  
Finite Fields ◽  
Module Structure ◽  
Cyclic Module ◽  
Dickson Polynomials

scholarly journals Fixed Points of the Dickson Polynomials of the Second Kind

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Adama Diene ◽  
Mohamed A. Salim
Keyword(s):  
Fixed Points ◽  
Finite Fields ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Dickson Polynomials ◽  
Necessary And Sufficient

The permutation behavior of Dickson polynomials of the first kind has been extensively studied, while such behavior for Dickson polynomials of the second kind is less known. Necessary and sufficient conditions for a polynomial of the second kind to be a permutation over some finite fields have been established by Cohen, Matthew, and Henderson. We introduce a new way to define these polynomials and determine the number of their fixed points.

scholarly journals Factors of Dickson polynomials over finite fields

2005 ◽  
Vol 11 (4) ◽  
pp. 724-737 ◽  
Author(s):  
Robert W. Fitzgerald ◽  
Joseph L. Yucas
Keyword(s):  
Finite Fields ◽  
Dickson Polynomials ◽  
Polynomials Over Finite Fields

scholarly journals Value sets of Dickson polynomials over finite fields

1988 ◽  
Vol 30 (3) ◽  
pp. 334-344 ◽  
Author(s):  
Wun-Seng Chou ◽  
Javier Gomez-Calderon ◽  
Gary L. Mullen
Keyword(s):  
Finite Fields ◽  
Dickson Polynomials ◽  
Polynomials Over Finite Fields ◽  
Value Sets
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