scholarly journals Character sums over Galois rings and primitive polynomials over finite fields

2004 ◽  
Vol 10 (1) ◽  
pp. 36-52 ◽  
Author(s):  
Fan Shuqin ◽  
Han Wenbao
Keyword(s):  
Finite Fields ◽  
Character Sums ◽  
Galois Rings ◽  
Primitive Polynomials ◽  
Polynomials Over Finite Fields

Some primitive polynomials over finite fields

2001 ◽  
Vol 21 (3) ◽  
pp. 412-416 ◽  
Author(s):  
Seunghwan Chang ◽  
June Bok Lee
Keyword(s):  
Finite Fields ◽  
Primitive Polynomials ◽  
Polynomials Over Finite Fields

scholarly journals On the number of primitive polynomials over finite fields

2005 ◽  
Vol 11 (1) ◽  
pp. 156-163 ◽  
Author(s):  
Yaotsu Chang ◽  
Wun-Seng Chou ◽  
Peter J.-S. Shiue
Keyword(s):  
Finite Fields ◽  
Primitive Polynomials ◽  
Polynomials Over Finite Fields

scholarly journals On primitive polynomials over finite fields

1989 ◽  
Vol 124 (2) ◽  
pp. 337-353 ◽  
Author(s):  
Dieter Jungnickel ◽  
Scott A Vanstone
Keyword(s):  
Finite Fields ◽  
Primitive Polynomials ◽  
Polynomials Over Finite Fields

Groups generated by iterations of polynomials over finite fields

2015 ◽  
Vol 59 (1) ◽  
pp. 235-245 ◽  
Author(s):  
Igor E. Shparlinski
Keyword(s):  
Lower Bound ◽  
Finite Field ◽  
Finite Fields ◽  
Mild Condition ◽  
Character Sums ◽  
Small Subgroup ◽  
Polynomials Over Finite Fields

AbstractGiven a finite field of q elements, we consider a trajectory of the map associated with a polynomial ]. Using bounds of character sums, under some mild condition on f, we show that for an appropriate constant C > 0 no N ⩾ Cq½ distinct consecutive elements of such a trajectory are contained in a small subgroup of , improving the trivial lower bound . Using a different technique, we also obtain a similar result for very small values of N. These results are multiplicative analogues of several recently obtained bounds on the length of intervals containing N distinct consecutive elements of such a trajectory.

Construction of primitive polynomials over finite fields

2020 ◽  
pp. 2150078
Author(s):  
Mahmood Alizadeh
Keyword(s):  
Finite Fields ◽  
Primitive Polynomial ◽  
Composition Methods ◽  
Primitive Polynomials ◽  
Polynomial Composition ◽  
Polynomials Over Finite Fields

In this paper, using the polynomial composition methods some computationally simple and explicit ways for constructing higher degrees primitive polynomials from a given primitive polynomial over [Formula: see text] are given.

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