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Hexiang Huang

Publications and source records attributed to Hexiang Huang.

8 recordsLinked to original sources
arXiv2026

Divisibility of Trace Codes

A linear code is said to be $\Delta$-divisible if the Hamming weights of all its codewords are divisible by $\Delta$. The $p$-adic valuation of a code is defined as the greatest integer $t$ such that the code is $p^t$-divisible. In this paper, we establish a divisibility criterion for trace codes. Specifically, this criterion provides a systematic method to determine the $p$-adic valuation of the associated trace code, thereby extending Ward's classical divisibility criterion from standard generating sets (or matrices) to generalized generator matrices over an extension field. Furthermore, we present two applications of our framework. The first application provides a concise proof of the celebrated divisibility results on semisimple Abelian codes established by Delsarte and McEliece. The second application establishes several explicit lower bounds on the $p$-adic valuation of the number of solutions over $\mathbb{F}_{q^m}$ (where $q = p^e$) to the Artin--Schreier type equation $ f(x_1,\ldots,x_k)=y^q-y $. In particular, under the coprime condition $\left(d,\frac{q^m-1}{q-1}\right)=1$, we determine the exact minimum $p$-adic valuation of the number of solutions when $f$ is restricted to homogeneous polynomials of degree $d$.

math.CO↗
arXiv2025

On the quantum chromatic number of Hamming and generalized Hadamard graphs

As a fundamental metric for quantifying quantum advantage in non-local games, the quantum chromatic number reveals the power of entanglement in distributed tasks. In this paper, we investigate this parameter for $q$-ary Hamming graphs and a generalization of Hadamard graphs. Our main results establish an exponential separation between the quantum and classical chromatic numbers for both graph families, and determine the exact quantum chromatic numbers in several regimes. Our analysis builds on known upper and lower bounds via modulus-one orthogonal representations and minimum eigenvalues, respectively. Previous results for Hamming graphs $H(n,q,d)$ were restricted to specific cases: the minimum eigenvalue was only identified for $d > (q-1)n/q$, while modulus-one orthogonal representations had only been constructed for the binary case ($q=2$) with $d \ge n/2$. In this work, we fill several gaps in the existing literature by developing a linear programming approach to construct modulus-one orthogonal representations for arbitrary relative distances, and using the trace method to determine the minimum eigenvalues in the regime where $d$ lies slightly below the threshold $(q-1)n/q$. For generalized Hadamard graphs over cyclic groups and finite fields, by determining their minimum eigenvalues, we show that the spectral lower bound matches the natural upper bound on the quantum chromatic number. On the classical side, we apply the method of forbidden intersection pattern of Frankl and R\"odl to obtain an exponential lower bound on the chromatic number, thereby quantifying the separation between the quantum and classical quantities.

math.CO↗
arXiv2025

Hybrid-supervised Hypergraph-enhanced Transformer for Micro-gesture Based Emotion Recognition

Micro-gestures are unconsciously performed body gestures that can convey the emotion states of humans and start to attract more research attention in the fields of human behavior understanding and affective computing as an emerging topic. However, the modeling of human emotion based on micro-gestures has not been explored sufficiently. In this work, we propose to recognize the emotion states based on the micro-gestures by reconstructing the behavior patterns with a hypergraph-enhanced Transformer in a hybrid-supervised framework. In the framework, hypergraph Transformer based encoder and decoder are separately designed by stacking the hypergraph-enhanced self-attention and multiscale temporal convolution modules. Especially, to better capture the subtle motion of micro-gestures, we construct a decoder with additional upsampling operations for a reconstruction task in a self-supervised learning manner. We further propose a hypergraph-enhanced self-attention module where the hyperedges between skeleton joints are gradually updated to present the relationships of body joints for modeling the subtle local motion. Lastly, for exploiting the relationship between the emotion states and local motion of micro-gestures, an emotion recognition head from the output of encoder is designed with a shallow architecture and learned in a supervised way. The end-to-end framework is jointly trained in a one-stage way by comprehensively utilizing self-reconstruction and supervision information. The proposed method is evaluated on two publicly available datasets, namely iMiGUE and SMG, and achieves the best performance under multiple metrics, which is superior to the existing methods.

cs.CV↗
arXiv2025

Divisibility of Griesmer Codes

In this paper, we consider Griesmer codes, namely those linear codes meeting the Griesmer bound. Let $C$ be an $[n,k,d]_q$ Griesmer code with $q=p^f$, where $p$ is a prime and $f\ge1$ is an integer. In 1998, Ward proved that for $q=p$, if $p^e|d$, then $p^e|\mathrm{wt}(c)$ for all $c\in C$. In this paper, we show that if $q^e|d$, then $C$ has a basis consisting of $k$ codewords such that the first $\min\left\{e+1,k\right\}$ of them span a Griesmer subcode with constant weight $d$ and any $k-1$ of them span a $[g_q(k-1,d),k-1,d]_q$ Griesmer subcode. Using the $p$-adic algebraic method together with this basis, we prove that if $q^e|d$, then $p^e|\mathrm{wt}(c)$ for all $c\in C$. Based on this fact, using the geometric approach with the aforementioned basis, we show that if $p^e|d$, then $\Delta |{\rm wt}(c)$ for all $c\in C$, where $\Delta=\left\lceil p^{e-(f-1)(q-2)}\right\rceil$.

math.CO↗
arXiv2024

A Multilingual Dataset and Empirical Validation for the Mutual Reinforcement Effect in Information Extraction

The Mutual Reinforcement Effect (MRE) describes a phenomenon in information extraction where word-level and sentence-level tasks can mutually improve each other when jointly modeled. While prior work has reported MRE in Japanese, its generality across languages and task settings has not been empirically validated, largely due to the lack of multilingual MRE datasets. To address this limitation, we introduce the Multilingual MRE Mix dataset (MMM), which consists of 21 sub-datasets covering English, Japanese, and Chinese. We propose an LLM-assisted dataset translation and alignment framework that significantly reduces manual annotation effort while preserving the structural requirements of MRE tasks. Building on MMM, we adopt a unified input-output framework to train an open-domain information extraction model and conduct extensive empirical studies, including full fine-tuning ablations and the construction of knowledgeable verbalizers based on MRE-mix data. Experimental results show that 76 percent of the MMM sub-datasets consistently exhibit the Mutual Reinforcement Effect across languages. These findings provide systematic empirical validation of MRE in multilingual settings and demonstrate its practical value for information extraction.

cs.CL↗
arXiv2023

The BCH Family of Storage Codes on Triangle-Free Graphs is of Unit Rate

Let $Γ$ be a simple connected graph on $n$ vertices, and let $C$ be a code of length $n$ whose coordinates are indexed by the vertices of $Γ$. We say that $C$ is a \textit{storage code} on $Γ$ if for any codeword $c \in C$, one can recover the information on each coordinate of $c$ by accessing its neighbors in $Γ$. The main problem here is to construct high-rate storage codes on triangle-free graphs. In this paper, we solve an open problem posed by Barg and Zémor in 2022, showing that the BCH family of storage codes is of unit rate. Furthermore, we generalize the construction of the BCH family and obtain more storage codes of unit rate on triangle-free graphs.

cs.IT↗
arXiv2023

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

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 collection of such assignments is called a storage code of length $|V|$ on $Γ$. In this paper we construct an infinite family of binary linear storage codes on triangle-free graphs with rates arbitrarily close to one.

math.CO↗