Some new classes of permutation trinomials over finite fields with even characteristic

Gupta, Rohit; Sharma, Rajendra K.

doi:10.1016/j.ffa.2016.05.004

Cited by 87 publications

(45 citation statements)

References 14 publications

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“…In the same paper, they also proposed the following two conjectures, which can be used to obtain two new classes of permutation trinomials with the form (1). More recent progress on permutation trinomials can be found in [2,6,7,8,9,10,12,13,14,15,16,20].…”

Section: Introductionmentioning

confidence: 99%

A note on permutation polynomials over finite fields

2017

Finite Fields and Their Applications

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Section: Introductionmentioning

confidence: 99%

A note on permutation polynomials over finite fields

2017

Finite Fields and Their Applications

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“…We end this section by discussin briefly two conjectures about permutation trinomials presented by Gupta and Sharma [5] and proved in [16,15]:…”

Section: On Some Conjectures On Permutation Polynomialsmentioning

confidence: 98%

Permutation polynomials, fractional polynomials, and algebraic curves

Bartoli

Giulietti

2018

Finite Fields and Their Applications

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In this note we prove a conjecture by Li, Qu, Li, and Fu on permutation trinomials over F 2k 3 . In addition, new examples and generalizations of some families of permutation polynomials of F 3 k and F 5 k are given. We also study permutation quadrinomials of type Ax q(q−1)+1 + Bx 2(q−1)+1 + Cx q + x. Our method is based on the investigation of an algebraic curve associated with a fractional polynomial over a finite field.

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“…If ab 4 +ab 2 +a 5 +a 3 b 6 = 0, i.e., (b 2 +b+a 2 +ab 3 ) 2 = 0 since a = 0. Then by (5), one obtains that b 6…”

Section: Proof Of Conjecturementioning

confidence: 99%

“…The construction of permutation polynomials with a simple algebraic form is an interesting research problem and it has already attracted researchers' much attention in recent years. By using certain techniques in dealing with equations or polynomials over finite fields, a number of permutation polynomials with a simple form have been obtained, the reader is referred to [3,5,6,7,8,10,12,16,23,24,26,27] and the references therein. Motivated by the observation that more than half of the known permutation binomials and trinomials were constructed from Niho exponents, Li and Helleseth [12] aimed to investigate permutation trinomials over F 2 n [x] of the form…”

Section: Introductionmentioning

confidence: 99%