Xiang-dong Hou

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20012023

most citedConnected Quandles Associated with Pointed Abelian Groups

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

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12 papers · 1 filter

math.CO2020

On the Number of Affine Equivalence Classes of Boolean Functions

Xiang-dong Hou

Let $R (r, n)$ be the $r$ th order Reed-Muller code of length $2^{n}$ . The affine linear group $AGL (n, F_{2})$ acts naturally on $R (r, n)$ . We derive two formulas concerning the…

math.CO2017

Optimal Binary Constant Weight Codes and Affine Linear Groups over Finite Fields

Xiang-dong Hou

Let $AGL (1, F_{q})$ be the affine linear group of dimension $1$ over a finite field $F_{q}$ . $AGL (1, F_{q})$ acts sharply 2-transitively on $F_{q}$ . Given $…

math.CO2017

On the DLW Conjectures

Xiang-dong Hou

In 2007, Dmytrenko, Lazebnik and Williford posed two related conjectures about polynomials over finite fields. Conjecture~1 is a claim about the uniqueness of certain monomial grap…

math.CO2016★ 1 cited

Permutation Polynomials of the form $X^{r} (a + X^{2 (q - 1)})$ --- A Nonexistence Result

Xiang-dong Hou

Let $f = X^{r} (a + X^{2 (q - 1)}) \in F_{q^{2}} [X]$ , where $a \in F_{q^{2}}^{*}$ and $r \geq 1$ . The parameters $(q, r, a)$ for which $f$ is a permutation polynomial (PP)…

math.CO2015★ 1 cited

Proof of a conjecture on monomial graphs

Xiang-dong Hou, Stephen D. Lappano, Felix Lazebnik

Let $e$ be a positive integer, $p$ be an odd prime, $q = p^{e}$ , and $F_{q}$ be the finite field of $q$ elements. Let $f, g \in F_{q} [X, Y]$ . The graph $G = G_{q} (f, g)$ is a biparti…

math.CO2014★ 2 cited

Switchings of semifield multiplications

Xiang-dong Hou, Ferruh Özbudak, Yue Zhou

Let $B (X, Y)$ be a polynomial over $F_{q^{n}}$ which defines an $F_{q}$ -bilinear form on the vector space $F_{q^{n}}$ , and let $ξ$ be a nonzero element in $\mat…

On the Number of Affine Equivalence Classes of Boolean Functions

Optimal Binary Constant Weight Codes and Affine Linear Groups over Finite Fields

On the DLW Conjectures

Permutation Polynomials of the form Xr(a+X2(q−1)) --- A Nonexistence Result

Proof of a conjecture on monomial graphs

Switchings of semifield multiplications

Permutation Polynomials of the form $X^{r} (a + X^{2 (q - 1)})$ --- A Nonexistence Result