Xiang-dong Hou

activity

20012023

most citedConnected Quandles Associated with Pointed Abelian Groups

21 citations · 75 across the 45 of their papers we have counts for

collaborators

45 papers

math.NT2023

Number of Equivalence Classes of Rational Functions over Finite Fields

Xiang-dong Hou

Two rational functions $f, g \in F_{q} (X)$ are said to be {\em equivalent} if there exist $ϕ, ψ \in F_{q} (X)$ of degree one such that $g = ϕ \circ f \circ ψ$ . We give an explicit formul…

math.NT2022

A Criterion for the Normality of Polynomials over Finite Fields Based on Their Coefficients

Xiang-dong Hou

An irreducible polynomial over $F_{q}$ is said to be normal over $F_{q}$ if its roots are linearly independent over $F_{q}$ . We show that there is a polynomial $h_n(X_1,\d…

math.RA2022

Some Algebraic Questions about the Reed-Muller Code

Xiang-dong Hou

Let $R_{q} (r, n)$ denote the $r$ th order Reed-Muller code of length $q^{n}$ over $F_{q}$ . We consider two algebraic questions about the Reed-Muller code. Let $H_q(r,n)=R_q(r,n)/R_q(r…

math.NT2022

A General Construction of Permutation Polynomials of $F_{q^{2}}$

Xiang-dong Hou, Vincenzo Pallozzi Lavorante

Let $r$ be a positive integer, $h (X) \in F_{q^{2}} [X]$ , and $μ_{q + 1}$ be the subgroup of order $q + 1$ of $F_{q^{2}}^{*}$ . It is well known that $X^{r} h (X^{q - 1})$ permutes $\Bbb F_{q…

math.NT2021

New Results on Permutation Binomials of Finite Fields

Xiang-dong Hou, Vincenzo Pallozzi Lavorante

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 bri…

math.RA2020

On a radical extension of the field of rational functions in several variables

Xiang-dong Hou, Christopher Sze

Let $F$ be a field and let $F (X_{1}, \dots, X_{n})$ be the field of rational functions in $n$ variables $X_{1}, \dots, X_{n}$ over $F$ . Let $T = X_{1} + \dots + X_{n} \in F (X_{1}, \dots, X_{n})$ and let $m$ b…

Number of Equivalence Classes of Rational Functions over Finite Fields

A Criterion for the Normality of Polynomials over Finite Fields Based on Their Coefficients

Some Algebraic Questions about the Reed-Muller Code

A General Construction of Permutation Polynomials of Fq2​

New Results on Permutation Binomials of Finite Fields

On a radical extension of the field of rational functions in several variables

A General Construction of Permutation Polynomials of $F_{q^{2}}$