Qing Xiang

activity

20032023

most citedCameron-Liebler Line Classes with parameter

x = \frac{( q + 1 ) ^{2}}{3}

13 citations · 73 across the 45 of their papers we have counts for

collaborators

Showing math.COShow all

42 papers · 1 filter

math.CO2023

Construction of storage codes of rates approaching one on triangle-free graphs

Hexiang Huang, Qing Xiang

Consider an assignment of bits to the vertices of a connected graph $Γ (V, E)$ with the property that the value of each vertex is a function of the values of its neighbors. A collec…

math.CO2022

Constructions of tight sets of the Hermitian polar space $\mc{H}(2r-1,q^2)$

Alice M. W. Hui, Weicong Li, Qing Xiang +1

In this paper, we construct two infinite families of tight sets with parameters $(q^{2 r - 2} - 1)$ and $(q^{2 r - 1} - q^{2 r - 2})$ , respectively, in the Hermitian polar space $\mathcal{H}(2r…

math.CO2021

Cyclic arcs of Singer type and strongly regular Cayley graphs over finite fields

Koji Momihara, Qing Xiang

In \cite{M18}, the first author gave a construction of strongly regular Cayley graphs on the additive group of finite fields by using three-valued Gauss periods. In particular, tog…

math.CO2020★ 13 cited

Cameron-Liebler Line Classes with parameter $x = \frac{( q + 1 ) ^{2}}{3}$

Tao Feng, Koji Momihara, Morgan Rodgers +2

Cameron-Liebler line classes were introduced in \cite{CL}, and motivated by a question about orbits of collineation groups of $\PG(3,q)$. These line classes have appeared in differ…

math.CO2019

On $m$ -ovoids of Symplectic Polar Spaces

Tao Feng, Ye Wang, Qing Xiang

In this paper, we develop a new method for constructing $m$ -ovoids in the symplectic polar space $\W(2r-1,\q)$ from some strongly regular Cayley graphs in \cite{Brouwer1999Journal}…

math.CO2019

Linear representations of finite geometries and associated LDPC codes

Peter Sin, Julien Sorci, Qing Xiang

The {\it linear representation} of a subset of a finite projective space is an incidence system of affine points and lines determined by the subset. In this paper we use character…

math.CO2019

A new family of Hadamard matrices of order $4 (2 q^{2} + 1)$

Ka Hin Leung, Koji Momihara, Qing Xiang

Let $q$ be a prime power of the form $q = 12 c^{2} + 4 c + 3$ with $c$ an arbitrary integer. In this paper we construct a difference family with parameters $(2 q^{2}; q^{2}, q^{2}, q^{2}, q^{2} - 1; 2 q^{2} - 2)$ …

math.CO2019

Generalized constructions of Menon-Hadamard difference sets

Koji Momihara, Qing Xiang

We revisit the problem of constructing Menon-Hadamard difference sets. In 1997, Wilson and Xiang gave a general framework for constructing Menon-Hadamard difference sets by using a…

math.CO2018★ 6 cited

Cyclotomy, difference sets, sequences with low correlation, strongly regular graphs, and related geometric substructures

Koji Momihara, Qi Wang, Qing Xiang

In this paper, we survey constructions of and nonexistence results on combinatorial/geometric structures which arise from unions of cyclotomic classes of finite fields. In particul…

math.CO2018★ 1 cited

The shift bound for abelian codes and generalizations of the Donoho-Stark uncertainty principle

Tao Feng, Henk D. L. Hollmann, Qing Xiang

Let $G$ be a finite abelian group. If $f: G\rightarrow \bC$ is a nonzero function with Fourier transform $\hf$, the Donoho-Stark uncertainty principle states that $|\supp(f)||\supp…

math.CO2018

Skew Hadamard difference families and skew Hadamard matrices

Koji Momihara, Qing Xiang

In this paper, we generalize classical constructions of skew Hadamard difference families with two or four blocks in the additive groups of finite fields given by Szekeres (1969, 1…

math.CO2017★ 3 cited

Strongly regular Cayley graphs from partitions of subdifference sets of the Singer difference sets

Koji Momihara, Qing Xiang

In this paper, we give a new lifting construction of "hyperbolic" type of strongly regular Cayley graphs. Also we give new constructions of strongly regular Cayley graphs over the…

math.CO2016

Resilience of ranks of higher inclusion matrices

Rafael Plaza, Qing Xiang

Let $n \geq r \geq s \geq 0$ be integers and $F$ a family of $r$ -subsets of $[n]$ . Let $W_{r, s}^{F}$ be the higher inclusion matrix of the subsets in ${\mathcal…

math.CO2016

New Bounds for Partial Spreads of $H (2 d - 1, q^{2})$ and Partial Ovoids of the Ree-Tits Octagon

Ferdinand Ihringer, Peter Sin, Qing Xiang

Two results are obtained that give upper bounds on partial spreads and partial ovoids respectively. The first result is that the size of a partial spread of the Hermitian polar spa…

math.CO2015★ 1 cited

A New Infinite Family of Hemisystems of the Hermitian Surface

John Bamberg, Melissa Lee, Koji Momihara +1

In this paper, we construct an infinite family of hemisystems of the Hermitian surface $H (3, q^{2})$ . In particular, we show that for every odd prime power $q$ congruent to $…

math.CO2015

The Smith group of the hypercube

David Chandler, Peter Sin, Qing Xiang

The $n$ -cube graph is the graph on the vertex set of $n$ -tuples of $0$ s and $1$ s, with two vertices joined by an edge if and only if the $n$ -tuples differ in exactly one component.…

math.CO2015

A family of $m$ -ovoids of parabolic quadrics

Tao Feng, Koji Momihara, Qing Xiang

We construct a family of $\frac{( q - 1 )}{2}$ -ovoids of $Q (4, q)$ , the parabolic quadric of $PG (4, q)$ , for $q \equiv 3 (mod 4)$ . The existence of $\frac{( q - 1 )}{2}$ -ovoids of $Q(…

math.CO2014

Three-valued Gauss periods, circulant weighing matrices and association schemes

Tao Feng, Koji Momihara, Qing Xiang

Gauss periods taking exactly two values are closely related to two-weight irreducible cyclic codes and strongly regular Cayley graphs. They have been extensively studied in the wor…

math.CO2014★ 2 cited

Cameron-Liebler line classes with parameter $x = \frac{q ^{2} - 1}{2}$

Tao Feng, Koji Momihara, Qing Xiang

In this paper, we give an algebraic construction of a new infinite family of Cameron-Liebler line classes with parameter $x = \frac{q ^{2} - 1}{2}$ for $q \equiv 5$ or $9 (mod 12)$ , which…

math.CO2014

The Smith and critical groups of Paley graphs

David Chandler, Peter Sin, Qing Xiang

There is a Paley graph for each prime power $q$ such that $q \equiv 1 (mod 4)$ . The vertex set is the field $F q$ and two vertices $x$ and $y$ are joined by an edge if and onl…

math.CO2012★ 2 cited

Lifting Constructions of Strongly Regular Cayley Graphs

Koji Momihara, Qing Xiang

We give two "lifting" constructions of strongly regular Cayley graphs. In the first construction we "lift" a cyclotomic strongly regular graph by using a subdifference set of the S…

math.CO2012★ 10 cited

Constructions of Strongly Regular Cayley Graphs and Skew Hadamard Difference Sets from Cyclotomic Classes

Tao Feng, Koji Momihara, Qing Xiang

In this paper, we give a construction of strongly regular Cayley graphs and a construction of skew Hadamard difference sets. Both constructions are based on choosing cyclotomic cla…

math.CO2012

Constructions of Strongly Regular Cayley Graphs Using Index Four Gauss Sums

Gennian Ge, Qing Xiang, Tao Yuan

We give a construction of strongly regular Cayley graphs on finite fields $\F_q$ by using union of cyclotomic classes and index 4 Gauss sums. In particular, we obtain two infinite…

math.CO2011

Cyclotomic Constructions of Skew Hadamard Difference Sets

Tao Feng, Qing Xiang

We revisit the old idea of constructing difference sets from cyclotomic classes. Two constructions of skew Hadamard difference sets are given in the additive groups of finite field…

Construction of storage codes of rates approaching one on triangle-free graphs

Constructions of tight sets of the Hermitian polar space $\mc{H}(2r-1,q^2)$

Cyclic arcs of Singer type and strongly regular Cayley graphs over finite fields

Cameron-Liebler Line Classes with parameter x=3(q+1)2​

On m-ovoids of Symplectic Polar Spaces

Linear representations of finite geometries and associated LDPC codes

A new family of Hadamard matrices of order 4(2q2+1)

Generalized constructions of Menon-Hadamard difference sets

Cyclotomy, difference sets, sequences with low correlation, strongly regular graphs, and related geometric substructures

The shift bound for abelian codes and generalizations of the Donoho-Stark uncertainty principle

Skew Hadamard difference families and skew Hadamard matrices

Strongly regular Cayley graphs from partitions of subdifference sets of the Singer difference sets

Resilience of ranks of higher inclusion matrices

New Bounds for Partial Spreads of H(2d−1,q2) and Partial Ovoids of the Ree-Tits Octagon

A New Infinite Family of Hemisystems of the Hermitian Surface

The Smith group of the hypercube

A family of m-ovoids of parabolic quadrics

Three-valued Gauss periods, circulant weighing matrices and association schemes

Cameron-Liebler line classes with parameter x=2q2−1​

The Smith and critical groups of Paley graphs

Lifting Constructions of Strongly Regular Cayley Graphs

Constructions of Strongly Regular Cayley Graphs and Skew Hadamard Difference Sets from Cyclotomic Classes

Constructions of Strongly Regular Cayley Graphs Using Index Four Gauss Sums

Cyclotomic Constructions of Skew Hadamard Difference Sets

Cameron-Liebler Line Classes with parameter $x = \frac{( q + 1 ) ^{2}}{3}$

On $m$ -ovoids of Symplectic Polar Spaces

A new family of Hadamard matrices of order $4 (2 q^{2} + 1)$

New Bounds for Partial Spreads of $H (2 d - 1, q^{2})$ and Partial Ovoids of the Ree-Tits Octagon

A family of $m$ -ovoids of parabolic quadrics

Cameron-Liebler line classes with parameter $x = \frac{q ^{2} - 1}{2}$