On the Number of Solutions of Equations of Dickson Polynomials Over Finite Fields

Chou, Wun Seng; Mullen, Gary L.; Wassermann, Bertram

doi:10.11650/twjm/1500404986

Cited by 9 publications

(11 citation statements)

References 1 publication

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“…then (3) has a nontrivial solution in F n q . Note that in some cases the existence of more than one solution can be deduced from Theorem 10 of [6], while in some other cases the lower bound of Theorem 10 of [6] is trivial, however, our Theorem 6 still applies. We illustrate the latter situation with an example.…”

Section: Equations With Dickson Polynomialsmentioning

confidence: 89%

“…Since for a = 0 we have D m (X, a) = X m , the equation (3) can be viewed as a generalization of the diagonal equation (1). Chou, Mullen, and Wassermann [6] used a character sum argument to give bounds for the number of solutions to (3) in F n q . See also [7] and [13] for some results on (3) with a 1 = · · · = a n , b 1 = · · · = b n = 1.…”

Section: Equations With Dickson Polynomialsmentioning

confidence: 99%

“…In order to generalize Theorem 4, we need the following result concerning the cardinality of the value set of D m (X, a) with a ∈ F * q (for a proof, see [5, Theorems 10 and 10 ′ ] or [9, Theorems 3.27 and 3.30]; see also [6,Theorem 7] for an alternative proof).…”

Section: Equations With Dickson Polynomialsmentioning

confidence: 99%

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On a theorem of Morlaye and Joly and its generalization

Baoulina

2019

European Journal of Combinatorics

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We show that a weaker version of the well-known theorem of Morlaye and Joly on diagonal equations is a simple consequence of a restricted variable version of the Chevalley-Warning theorem. Moreover, we extend the result of Morlaye and Joly to the case of an equation of the form b 1 D m1 (X 1 , a 1 ) + · · · + b n D mn (X n , a n ) = c, where D m1 (X 1 , a 1 ), . . . , D mn (X n , a n ) are Dickson polynomials.

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Section: Equations With Dickson Polynomialsmentioning

confidence: 89%

Section: Equations With Dickson Polynomialsmentioning

confidence: 99%

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On a theorem of Morlaye and Joly and its generalization

Baoulina

2019

European Journal of Combinatorics

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“…It turns out an analogous preimage-counting statement holds when a = 0. Chou, Mullen, and Wassermann in [4] used a character sum argument to calculate the following.…”

Section: Introductionmentioning

confidence: 99%

Moment subset sums over finite fields

Lai

Marino

Robinson

et al. 2020

Finite Fields and Their Applications

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The k-subset sum problem over finite fields is a classical NPcomplete problem. Motivated by coding theory applications, a more complex problem is the higher m-th moment k-subset sum problem over finite fields. We show that there is a deterministic polynomial time algorithm for the mth moment k-subset sum problem over finite fields for each fixed m when the evaluation set is the image set of a monomial or Dickson polynomial of any degree n. In the classical case m = 1, this recovers previous results of Nguyen-Wang (the case m = 1, p > 2) [24] and the results of Choe-Choe (the case m = 1, p = 2) [3].

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“…D. Gomez and A. Winterhof [11] have considered an analogue of the Waring problem for Dickson polynomials over F q , that is, the question of the existence and estimation of a positive integer s such that the equation is solvable for any c ∈ F q ; see also [3].…”

Section: Introductionmentioning

confidence: 99%