scholarly journals Determination of a type of permutation trinomials over finite fields

2014 ◽  
Vol 166 (3) ◽  
pp. 253-278 ◽  
Author(s):  
Xiang-dong Hou
Keyword(s):  
Finite Fields ◽  
Permutation Trinomials

scholarly journals Determination of a class of permutation trinomials in characteristic three

2020 ◽  
Vol 61 ◽  
pp. 101596 ◽  
Author(s):  
Xiang-dong Hou ◽  
Ziran Tu ◽  
Xiangyong Zeng
Keyword(s):  
Permutation Trinomials

scholarly journals Combinatorics on Finite Fields: the Sign Repartition for the Quadratic Residues

2014 ◽  
Vol 22 (1) ◽  
pp. 41-44
Author(s):  
Şerban Bărcănescu
Keyword(s):  
Finite Fields ◽  
Class Number ◽  
Quadratic Extensions ◽  
Quadratic Residues

AbstractIn the present paper we present the equivalence between the combinatorial determination of the sign repartition for the quadratic residues and non-residues to the computation of the class number of certain quadratic extensions of the field of rationals.

scholarly journals Determination of a type of permutation binomials over finite fields

2015 ◽  
Vol 147 ◽  
pp. 14-23 ◽  
Author(s):  
Xiang-Dong Hou ◽  
Stephen D. Lappano
Keyword(s):  
Finite Fields

scholarly journals Construction and Determination of Irreducible Polynomials in Galois elds, GF(2m)

2019 ◽  
pp. 1-6
Author(s):  
Abraham Aidoo ◽  
Kwasi Baah Gyam ◽  
Fengfan Yang
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Monic Polynomial ◽  
Galois Field ◽  
Irreducible Polynomials ◽  
Primitive Polynomials

This work is about Construction of Irreducible Polynomials in Finite fields. We defined some terms in the Galois field that led us to the construction of the polynomials in the GF(2m). We discussed the following in the text; irreducible polynomials, monic polynomial, primitive polynomials, eld, Galois eld or nite elds, and the order of a finite field. We found all the polynomials in $$F_2[x]$$ that is, $$P(x) =\sum_{i=1}^m a_ix^i : a_i \in F_2$$ with $$a_m \neq 0$$ for some degree $m$ whichled us to determine the number of irreducible polynomials generally at any degree in $$F_2[x]$$.

scholarly journals A class of permutation trinomials over finite fields

2014 ◽  
Vol 162 (1) ◽  
pp. 51-64 ◽  
Author(s):  
Xiang-dong Hou
Keyword(s):  
Finite Fields ◽  
Permutation Trinomials
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