相关论文: Relative Generalized Rank Weight of Linear Codes a…
Improving the generalization ability of modern deep neural networks (DNNs) is a fundamental challenge in machine learning. Two branches of methods have been proposed to seek flat minima and improve generalization: one led by sharpness-aware…
The order bound for the minimum distance of algebraic geometry codes was originally defined for the duals of one-point codes and later generalized for arbitrary algebraic geometry codes. Another bound of order type for the minimum distance…
Distributed and cloud storage systems are used to reliably store large-scale data. Erasure codes have been recently proposed and used in real-world distributed and cloud storage systems such as Google File System, Microsoft Azure Storage,…
For $d\in\{5,6\}$, we classify arrangements of $d + 2$ points in $\mathbf{RP}^{d-1}$ for which the minimum distance is as large as possible. To do so, we leverage ideas from matrix and convex analysis to determine the best possible codes…
In network communications, information transmission often encounters wiretapping attacks. Secure network coding is introduced to prevent information from being leaked to adversaries. The investigation of performance bounds on the numbers of…
In this paper, a class of two-weight and three-weight linear codes over $\gf(p)$ is constructed, and their application in secret sharing is investigated. Some of the linear codes obtained are optimal in the sense that they meet certain…
Linear codes with few weights have applications in consumer electronics, communication, data storage system, secret sharing, authentication codes, association schemes, and strongly regular graphs. This paper first generalizes the method of…
The sim-to-real gap, which represents the disparity between training and testing environments, poses a significant challenge in reinforcement learning (RL). A promising approach to addressing this challenge is distributionally robust RL,…
The wide deployment of deep neural networks, though achieving great success in many domains, has severe safety and reliability concerns. Existing adversarial attack generation and automatic verification techniques cannot formally verify…
As an important coding scheme in modern distributed storage systems, locally repairable codes (LRCs) have attracted a lot of attentions from perspectives of both practical applications and theoretical research. As a major topic in the…
In real-world networks, predicting the weight (strength) of links is as crucial as predicting the existence of the links themselves. Previous studies have primarily used shallow graph features for link weight prediction, limiting the…
Proximity gaps and correlated agreement have become central tools in the analysis of interactive oracle proofs of proximity (IOPPs) and code-based SNARKs. Informally, a proximity-gap statement says that for a structured set of words -- such…
We consider the rack-aware storage system where $n=\bar{n}u$ nodes are organized in $\bar{n}$ racks each containing $u$ nodes, and any $k=\bar{k}u+u_0~(0\leq u_0<u)$ nodes can retrieve the original data file. More importantly, the…
Few-weight codes over finite chain rings are associated with combinatorial objects such as strongly regular graphs (SRGs), strongly walk-regular graphs (SWRGs) and finite geometries, and are also widely used in data storage systems and…
Let $G=(V,E)$ be a simple graph with $|V|=n$ nodes and $|E|=m$ links, a subset $K \subseteq V$ of \emph{terminals}, a vector $p=(p_1,...,p_m) \in [0,1]^m$ and a positive integer $d$, called \emph{diameter}. We assume nodes are perfect but…
Reduced rank regression (RRR) is a fundamental tool for modeling multiple responses through low-dimensional latent structures, offering both interpretability and strong predictive performance in high-dimensional settings. Classical RRR…
RankSign [GRSZ14a] is a code-based signature scheme proposed to the NIST competition for quantum-safe cryptography [AGHRZ17] and, moreover, is a fundamental building block of a new Identity-Based-Encryption (IBE) [GHPT17a]. This signature…
The minimum distance of a code is an important concept in information theory. Hence, computing the minimum distance of a code with a minimum computational cost is a crucial process to many problems in this area. In this paper, we present…
Reduced rank regression (RRR) is a statistical method for finding a low-dimensional linear mapping between a set of high-dimensional inputs and outputs. In recent years, RRR has found numerous applications in neuroscience, in particular for…
When a node in a distributed storage system fails, it needs to be promptly repaired to maintain system integrity. While typical erasure codes can provide a significant storage advantage over replication, they suffer from poor repair…