Searcharxiv⌕ Search

arXiv subjects

Haiyan Zhou

Publications and source records attributed to Haiyan Zhou.

11 recordsLinked to original sources
arXiv2026

Galois Hulls of Generalized Roth-Lempel Codes and Their Applications to EAQECCs

The dimension of a Galois hull is an important parameter in the construction of entanglement-assisted quantum error-correcting codes. In this paper, we study generalized Roth-Lempel (GRL) codes with prescribed Galois hull dimensions over finite fields of arbitrary characteristic. We develop a common construction method based on normalized Lagrange coefficients and suitable choices of column multipliers, and obtain six explicit constructions from multiplicative cosets, trace fibers, additive-subspace cosets, and mixed additive--multiplicative fibers. For extension sizes $s=2$ and $s=3$, we construct MDS and AMDS GRL codes with Galois hulls of specific dimensions. The resulting codes provide EAQECCs with explicit dimension, entanglement consumption, and relatively large minimum distance. Taking zero-dimensional hulls also gives Hermitian LCD GRL codes and the corresponding maximally entangled EAQECCs.

cs.IT↗
arXiv2026

On Twisted Roth-Lempel Codes

In 1989, Roth and Lempel constructed a well-known family of non-Reed-Solomon maximum distance separable (MDS) codes. For decades, this family of codes has attracted extensive research attention due to its algebraic structure, low-complexity decoding, and broad applications in cryptography and data storage. In this paper, we present a class of twisted Roth-Lempel codes. We investigate their minimum distance, MDS and NMDS properties. Specifically, we determine the necessary and sufficient conditions for the TRL codes to have minimum distance n-k or n-k+1. Furthermore, we determine the necessary and sufficient conditions for the TRL code to be an MDS or NMDS code. Moreover, we show that the dimension of the Schur square of the TRL code is at least 2k+1, and thus the TRL code is a non-RS code inequivalent to the corresponding RL code.

cs.IT↗
arXiv2026

Generalized Roth--Lempel Codes: NMDS Characterization, Hermitian Self-Orthogonality, and Quantum Constructions

In their seminal 1989 work (IEEE Trans. Inf. Theory 35(3):655-657), Roth and Lempel constructed a well-known family of non-Reed-Solomon maximum distance separable (MDS) codes. For decades, this family of codes has attracted extensive research attention due to its algebraic structure, low-complexity decoding, and broad applications in cryptography and data storage. Most recently, in 2025, the generalized Roth-Lempel (GRL) framework unifies Roth-Lempel codes and its extensions under a flexible algebraic structure. However, explicit criteria for the near-MDS (NMDS) property of GRL codes have not been established, and no systematic construction of Hermitian self-orthogonal GRL codes has been reported, limiting their deployment in classical and quantum error correction. In this work, we make three contributions to address these gaps. First, we give explicit necessary and sufficient conditions for the NMDS property of the two most widely used subclasses of GRL codes. Second, we construct four new families of Hermitian self-orthogonal codes from GRL codes. Two of these families are NMDS, with parameters not covered by existing Hermitian self-orthogonal NMDS codes. Third, based on the proposed Hermitian self-orthogonal GRL codes, we construct four families of quantum GRL codes, including two infinite families of quantum NMDS codes that attain the quantum Singleton bound minus one. Compared to the known quantum error-correcting codes, we obtain many new or improved quantum error-correcting codes. This work bridges the gap between classical GRL code families and quantum error-correction applications.

cs.IT↗
arXiv2025

Training Together, Diagnosing Better: Federated Learning for Collagen VI-Related Dystrophies

The application of Machine Learning (ML) to the diagnosis of rare diseases, such as collagen VI-related dystrophies (COL6-RD), is fundamentally limited by the scarcity and fragmentation of available data. Attempts to expand sampling across hospitals, institutions, or countries with differing regulations face severe privacy, regulatory, and logistical obstacles that are often difficult to overcome. The Federated Learning (FL) provides a promising solution by enabling collaborative model training across decentralized datasets while keeping patient data local and private. Here, we report a novel global FL initiative using the Sherpa.ai FL platform, which leverages FL across distributed datasets in two international organizations for the diagnosis of COL6-RD, using collagen VI immunofluorescence microscopy images from patient-derived fibroblast cultures. Our solution resulted in an ML model capable of classifying collagen VI patient images into the three primary pathogenic mechanism groups associated with COL6-RD: exon skipping, glycine substitution, and pseudoexon insertion. This new approach achieved an F1-score of 0.82, outperforming single-organization models (0.57-0.75). These results demonstrate that FL substantially improves diagnostic utility and generalizability compared to isolated institutional models. Beyond enabling more accurate diagnosis, we anticipate that this approach will support the interpretation of variants of uncertain significance and guide the prioritization of sequencing strategies to identify novel pathogenic variants.

cs.LG↗
arXiv2025

Construction of MDS Euclidean Self-Dual Codes via Multiple Subsets

MDS self-dual codes have good algebraic structure, and their parameters are completely determined by the code length. In recent years, the construction of MDS Euclidean self-dual codes with new lengths has become an important issue in coding theory. In this paper, we are committed to constructing new MDS Euclidean self-dual codes via generalized Reed-Solomon (GRS) codes and their extended (EGRS) codes. The main effort of our constructions is to find suitable subsets of finite fields as the evaluation sets, ensuring that the corresponding (extended) GRS codes are Euclidean self-dual. Firstly, we present a method for selecting evaluation sets from multiple intersecting subsets and provide a theorem to guarantee that the chosen evaluation sets meet the desired criteria. Secondly, based on this theorem, we construct six new classes of MDS Euclidean self-dual codes using the norm function, as well as the union of three multiplicity subgroups and their cosets respectively. Finally, in our constructions, the proportion of possible MDS Euclidean self-dual codes exceeds 85\%, which is much higher than previously reported results.

cs.IT↗
arXiv2024

Large Sets of Quasi-Complementary Sequences From Polynomials over Finite Fields and Gaussian Sums

Perfect complementary sequence sets (PCSSs) are widely used in multi-carrier code-division multiple-access (MC-CDMA) communication systems. However, the set size of a PCSS is upper bounded by the number of row sequences of each two-dimensional matrix in the PCSS. Then quasi-complementary sequence sets (QCSSs) were proposed to support more users in MC-CDMA communications. For practical applications, it is desirable to construct an $(M,K,N,\vartheta_{\max})$-QCSS with $M$ as large as possible and $\vartheta_{max}$ as small as possible, where $M$ is the number of matrices with $K$ rows and $N$ columns in the set and $\vartheta_{\max}$ denotes its periodic tolerance. There exists a tradeoff among these parameters. Constructing QCSSs achieving or nearly achieving the known correlation lower bound has been an interesting research topic. Up to now, only a few constructions of asymptotically optimal or near-optimal periodic QCSSs have been reported in the literature. In this paper, based on polynomials over finite fields and Gaussian sums, we construct five new families of asymptotically optimal or near-optimal periodic QCSSs with large set sizes and low periodic tolerances. These families of QCSSs have set size $Θ(K^2)$ or $Θ(K^3)$ and flock size $K$. To the best of our knowledge, only a small amount of known families of periodic QCSSs with set size $Θ(K^2)$ have been constructed and most of other known periodic QCSSs have set sizes much smaller than $Θ(K^2)$. Our new constructed periodic QCSSs with set size $Θ(K^2)$ and flock size $K$ have the best parameters among all known ones. They have larger set sizes or lower periodic tolerances. The periodic QCSSs with set size $Θ(K^3)$ and flock size $K$ constructed in this paper have the largest set size among all known families of asymptotically optimal or near-optimal periodic QCSSs.

cs.IT↗
arXiv2024

New families of non-Reed-Solomon MDS codes

MDS codes have garnered significant attention due to their wide applications in practice. To date, most known MDS codes are equivalent to Reed-Solomon codes. The construction of non-Reed-Solomon (non-RS) type MDS codes has emerged as an intriguing and important problem in both coding theory and finite geometry. Although some constructions of non-RS type MDS codes have been presented in the literature, the parameters of these MDS codes remain subject to strict constraints. In this paper, we introduce a general framework of constructing $[n,k]$ MDS codes using the idea of selecting a suitable set of evaluation polynomials and a set of evaluation points such that all nonzero polynomials have at most $k-1$ zeros in the evaluation set. Moreover, these MDS codes can be proved to be non-Reed-Solomon by computing their Schur squares. Furthermore, several explicit constructions of non-RS MDS codes are given by converting to combinatorial problems. As a result, new families of non-RS MDS codes with much more flexible lengths can be obtained and most of them are not covered by the known results.

cs.IT↗
arXiv2022

Self-supervised Group Meiosis Contrastive Learning for EEG-Based Emotion Recognition

The progress of EEG-based emotion recognition has received widespread attention from the fields of human-machine interactions and cognitive science in recent years. However, how to recognize emotions with limited labels has become a new research and application bottleneck. To address the issue, this paper proposes a Self-supervised Group Meiosis Contrastive learning framework (SGMC) based on the stimuli consistent EEG signals in human being. In the SGMC, a novel genetics-inspired data augmentation method, named Meiosis, is developed. It takes advantage of the alignment of stimuli among the EEG samples in a group for generating augmented groups by pairing, cross exchanging, and separating. And the model adopts a group projector to extract group-level feature representations from group EEG samples triggered by the same emotion video stimuli. Then contrastive learning is employed to maximize the similarity of group-level representations of augmented groups with the same stimuli. The SGMC achieves the state-of-the-art emotion recognition results on the publicly available DEAP dataset with an accuracy of 94.72% and 95.68% in valence and arousal dimensions, and also reaches competitive performance on the public SEED dataset with an accuracy of 94.04%. It is worthy of noting that the SGMC shows significant performance even when using limited labels. Moreover, the results of feature visualization suggest that the model might have learned video-level emotion-related feature representations to improve emotion recognition. And the effects of group size are further evaluated in the hyper parametric analysis. Finally, a control experiment and ablation study are carried out to examine the rationality of architecture. The code is provided publicly online.

eess.SP↗
arXiv2017

On jumped Wenger graphs

In this paper we introduce a new infinite class of bipartite graphs, called jumped Wenger graphs, which are closely related to Wenger graphs. An tight upper bound of the diameter and the exact girth of a jumped Wenger graph $J_m(q, i, j )$ for integers $i, j$, $1\leq i <j \leq m+2$, are determined. In particular, the exact diameter of the jumped Wenger graph $J_m(q, i, j)$ if $(i, j)=(m,m+2), (m+1,m+2)$ or $(m,m+1)$ is also obtained.

math.CO↗
arXiv2017

Counting Polynomials with Distinct Zeros in Finite Fields

Let $\mathbb{F}_q$ be a finite field with $q=p^e$ elements, where $p$ is a prime and $e\geq 1$ is an integer. Let $\ell<n$ be two positive integers. Fix a monic polynomial $u(x)=x^n +u_{n-1}x^{n-1}+\cdots +u_{\ell+1}x^{\ell+1} \in \mathbb{F}_q[x]$ of degree $n$ and consider all degree $n$ monic polynomials of the form $$f(x) = u(x) + v_\ell(x), \ v_\ell(x)=a_\ell x^\ell+a_{\ell-1}x^{\ell-1}+\cdots+a_1x+a_0\in \mathbb{F}_q[x].$$ For integer $0\leq k \leq {\rm min}\{n,q\}$, let $N_k(u(x),\ell)$ denote the total number of $v_\ell(x)$ such that $u(x)+v_\ell(x)$ has exactly $k$ distinct roots in $\mathbb{F}_q$, i.e. $$N_k(u(x),\ell)=|\{f(x)=u(x)+v_l(x)\ |\ f(x)\ {\rm has\ exactly}\ k\ {\rm distinct\ zeros\ in}\ \mathbb{F}_q\}|.$$ In this paper, we obtain explicit combinatorial formulae for $N_k(u(x),\ell)$ when $n-\ell$ is small, namely when $n-\ell= 1, 2, 3$. As an application, we define two kinds of Wenger graphs called jumped Wenger graphs and obtain their explicit spectrum.

math.NT↗