相关论文: Weighted external difference families and R-optima…

It is well-known that the dimension of optimal anticodes in the rank-metric is divisible by the maximum m between the number of rows and columns of the matrices. Moreover, for a fixed k divisible by m, optimal rank-metric anticodes are the…

The classical family of $[n,k]_q$ Reed-Solomon codes over a field $\F_q$ consist of the evaluations of polynomials $f \in \F_q[X]$ of degree $< k$ at $n$ distinct field elements. In this work, we consider a closely related family of codes,…

Linear codes with few weights have applications in secret sharing, authentication codes, association schemes and strongly regular graphs. In this paper, several classes of $t$-weight linear codes over ${\mathbb F}_{q}$ are presented with…

In the realm of rank-metric codes, Maximum Rank Distance (MRD) codes are optimal algebraic structures attaining the Singleton-like bound. A major open problem in this field is determining whether an MRD code can be extended to a longer one…

Neural networks are susceptible to artificially designed adversarial perturbations. Recent efforts have shown that imposing certain modifications on classification layer can improve the robustness of the neural networks. In this paper, we…

Though deep neural networks have achieved significant progress on various tasks, often enhanced by model ensemble, existing high-performance models can be vulnerable to adversarial attacks. Many efforts have been devoted to enhancing the…

In this paper, we consider hybrid beamforming designs for multiuser massive multiple-input multiple-output (MIMO)-orthogonal frequency division multiplexing (OFDM) systems. Aiming at maximizing the weighted spectral efficiency, we propose…

We study a class of realistic computer vision settings wherein one can influence the design of the objects being recognized. We develop a framework that leverages this capability to significantly improve vision models' performance and…

This paper presents encoding and decoding algorithms for several families of optimal rank metric codes whose codes are in restricted forms of symmetric, alternating and Hermitian matrices. First, we show the evaluation encoding is the right…

We present FACADE, a novel probabilistic and geometric framework designed for unsupervised mechanistic anomaly detection in deep neural networks. Its primary goal is advancing the understanding and mitigation of adversarial attacks. FACADE…

We provide a comprehensive overview of the fundamental structural properties of weighted projective Reed-Muller codes. We give a recursive construction for these codes, under some conditions for the weights, and we use it to derive bounds…

A characterization of a class of optimal three-weight cyclic codes of dimension 3 over any finite field was recently presented in [10]. Shortly after this, a generalization for the sufficient numerical conditions of such characterization…

The Gromov-Wasserstein (GW) distances define a family of metrics, based on ideas from optimal transport, which enable comparisons between probability measures defined on distinct metric spaces. They are particularly useful in areas such as…

Gleason's 1970 theorem on weight enumerators of self-dual codes has played a crucial role for research in coding theory during the last four decades. Plenty of generalizations have been proved but, to our knowledge, they are all based on…

Strong difference families are an interesting class of discrete structures which can be used to derive relative difference families. Relative difference families are closely related to $2$-designs, and have applications in constructions for…

Let $G$ be a directed graph associated with a weight $w: E(G) \rightarrow R^+$. For an edge-cut $Q$ of $G$, the average weight of $Q$ is denoted and defined as $w_{ave}(Q)=\frac{\sum_{e\in Q}w(e)}{|Q|}$. An edge-cut of optimal average…

A connected undirected graph $G = (V,E)$ is lower conformally rigid if uniform edge weights maximize the second smallest Laplacian eigenvalue $\lambda_2(w)$ over all normalized edge weights $w$, and upper conformally rigid if uniform edge…

The Reed-Muller codes are a family of error-correcting codes that have been widely studied in coding theory. In 2020, Wei Yan and Sian-Jheng Lin introduced a variant of Reed-Muller codes so called symmetric Reed-Muller codes. We investigate…

For any affine-variety code we show how to construct an ideal whose solutions correspond to codewords with any assigned weight. We classify completely the intersections of the Hermitian curve with lines and parabolas (in the…

In \cite{shi2022few-weight}, Shi and Li studied $\mathcal{C}_D$-codes over the ring $\mathcal{R}:=\mathbb{F}_2[x,y]/\langle x^2, y^2, xy-yx\rangle$ and their binary Gray images, where $D$ is derived using certain simplicial complexes. We…