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On a Class of Permutation Trinomials in Characteristic 2 [article]

Xiang-dong Hou
2018 arXiv   pre-print
Recently, Tu, Zeng, Li, and Helleseth considered trinomials of the form f(X)=X+aX^q(q-1)+1+bX^2(q-1)+1∈ F_q^2[X], where q is even and a,b∈ F_q^2^*.  ...  They found sufficient conditions on a,b for f to be a permutation polynomial (PP) of F_q^2 and they conjectured that the sufficient conditions are also necessary.  ...  Tu, X. Zeng, C. Li, T. Helleseth, A class of new permutation trinomials, Finite Fields Appl. 50 (2018), 178 – 195. [11] Q.  ... 
arXiv:1803.04071v1 fatcat:nwj3j3jgcnfwtmwf6bhuakeoz4

New Permutation Trinomials Constructed from Fractional Polynomials [article]

Kangquan Li, Longjiang Qu, Chao Li, Shaojing Fu
2016 arXiv   pre-print
Distinct from most of the known permutation trinomials which are with fixed exponents, our results are some general classes of permutation trinomials with one parameter in the exponents.  ...  In the present paper, six new classes of permutation trinomials over finite fields of even characteristic are constructed from six fractional polynomials.  ...  In [28, Corollary 1.4 ], there was one class of permutation trinomial (see Theorem 2.3 in Section 2), which included two permutation trinomials raised as conjectures by Tu, Zeng, Hu and Li [25] .  ... 
arXiv:1605.06216v1 fatcat:t4q2k4drhvhcjbbib2whhw4po4

A Class of Binomial Permutation Polynomials [article]

Ziran Tu, Xiangyong Zeng, Lei Hu, Chunlei Li
2013 arXiv   pre-print
As a consequence, many classes of binomial permutation polynomials and monomial complete permutation polynomials are obtained. The exponents in these monomials are of Niho type.  ...  In this note, a criterion for a class of binomials to be permutation polynomials is proposed.  ...  Several classes of binomial permutation polynomials and monomial complete permutation polynomials are obtained. A conjecture on two classes of trinomials is presented in Section 4.  ... 
arXiv:1310.0337v1 fatcat:ma2hxg3cybhnnlzcjyo3go7kqu

On a conjecture about a class of permutation trinomials [article]

Daniele Bartoli
2017 arXiv   pre-print
We prove a conjecture by Tu, Zeng, Li, and Helleseth concerning trinomials f_α,β(x)= x + α x^q(q-1)+1 + β x^2(q-1)+1∈F_q^2[x], αβ≠ 0, q even, characterizing all the pairs (α,β)∈F_q^2^2 for which f_α,β(  ...  x) is a permutation of F_q^2.  ...  Acknowledgments The author was partially supported by the Italian Ministero dell'Istruzione, dell'Università e della Ricerca (MIUR) and by the Gruppo Nazionale per le Strutture Algebriche, Geometriche  ... 
arXiv:1712.10017v1 fatcat:wirwq6rzqrfejelk5avfsyxen4

New Results on Permutation Binomials of Finite Fields [article]

Xiang-dong Hou, Vincenzo Pallozzi Lavorante
2022 arXiv   pre-print
After a brief review of existing results on permutation binomials of finite fields, we introduce the notion of equivalence among permutation binomials (PBs) and describe how to bring a PB to its canonical  ...  We then focus on PBs of F_q^2 of the form X^n(X^d(q-1)+a), where n and d are positive integers and a∈ F_q^2^*.  ...  Hou, Determination of a type of permutation trinomials over finite fields, II, Finite Fields Appl. 35 (2015), 16 – 35. [4] X.  ... 
arXiv:2111.06533v2 fatcat:a7mavm2iw5e4jbgkgnmnckyc6m

2020 Index IEEE Transactions on Circuits and Systems I: Regular Papers Vol. 67

2020 IEEE Transactions on Circuits and Systems Part 1: Regular Papers  
., +, TCSI June 2020 1976-1988 On the Complexity of Hybrid n-Term Karatsuba Multiplier for Trinomials.  ...  ., +, TCSI July 2020 2297-2304 On the Complexity of Hybrid n-Term Karatsuba Multiplier for Trinomials.  ...  ., +, TCSI Feb. 2020 634-646 Histograms Linearity Theory of Stochastic Phase-Interpolation Time-to-Digital Converter. Gammoh, K., +,  ... 
doi:10.1109/tcsi.2021.3055003 fatcat:kbmst5td2bbvtl7vpbj3knnkri

Italian Journal of Pure and Applied Mathematics Papers Abstracts

2014 unpublished
(pp. 433-448) OD-CHARACTERIZATION OF ALTERNATING GROUP OF DEGREE p + 3 Yanxiong Yan, Yu Zeng, Haijing Xu, Guiyun Chen Let A p+3 be the alternating group of degree p + 3, where p is a prime, p + 4 is a  ...  When G is C 4 it is known, but unpublished in a journal, that r t (C 4 ; 2) = 3.  ... 
fatcat:ad6svqy6nvenpmg3es6fyox73q

Italian Journal of Pure and Applied Mathematics EDITOR-IN-CHIEF Piergiulio Corsini Editorial Board F O R U M EDITOR-IN-CHIEF VICE-CHIEFS Italian Journal of Pure and Applied Mathematics EDITOR-IN-CHIEF Vice-CHIEFS Managing Board Editorial Board Italian Journal of Pure and Applied Mathematics-N. 31-2013

Saeid Abbasbandy, Reza Ameri, Luisa Arlotti, Krassimir Atanassov, Malvina Baica, Federico Bartolozzi, Rajabali Borzooei, Carlo Cecchini, Gui-Yun Chen, Domenico Chillemi, Stephen Comer, Irina Cristea (+201 others)
2013 unpublished
This work was completed while the corresponding author was a visitor at the School of Mathematical Sciences, Dublin Institute of Technology. The author would like to thank Prof. B.  ...  The author is thankful to the referee for his/her several valuable suggestions which improved the presentation of the paper. Acknowledgment.  ...  ( c ) c |T (A)| = 3; one of the types is minimal and the other two types are maximal. then x 2 2 = ax, y 2 = xy = yx = 0 for some rational number a. Proof. See [4, Lemma 3].  ... 
fatcat:aooxh5zrirallcfxmrepiuv3ta