Related papers: Construction of Turbo Code Interleavers from 3-Reg…

This paper is concerned with list decoding of $2$-interleaved binary alternant codes. The principle of the proposed algorithm is based on a combination of a list decoding algorithm for (interleaved) Reed-Solomon codes and an algorithm for…

Both horizontal interleaving as well as the sum-rank metric are currently attractive topics in the field of code-based cryptography, as they could mitigate the problem of large key sizes. In contrast to vertical interleaving, where…

We consider the problem of high-dimensional Ising (graphical) model selection. We propose a simple algorithm for structure estimation based on the thresholding of the empirical conditional variation distances. We introduce a novel criterion…

The robust and safe operation of automated vehicles underscores the critical need for detailed and accurate topological maps. At the heart of this requirement is the construction of lane graphs, which provide essential information on lane…

We generalize a construction of non-binary quantum LDPC codes over $\F_{2^m}$ due to \cite{KHIS11a} and apply it in particular to toric codes. We obtain in this way not only codes with better rates than toric codes but also improve…

In this paper, we propose an intermittent communication framework for mobile robot networks. Specifically, we consider robots that move along the edges of a connected mobility graph and communicate only when they meet at the nodes of that…

One- and two-dimensional bilayer systems are examples of ultra-tunable quantum materials that are considered as the basis for the new generation of electronic and photonic devices. Here we develop a general theory of the electron band…

Tilings of the hyperbolic plane are of significant interest among many branches of mathematics, physics and computer science. Yet, their construction remains a non-trivial task. Current approaches primarily use tree-based recursive…

Isolated training with Gaussian priors (TGP) of the component autoencoders of turbo-autoencoder architectures enables faster, more consistent training and better generalization to arbitrary decoding iterations than training based on deep…

Interconnection networks provide an effective mechanism for exchanging data between processors in a parallel computing system. One of the most efficient interconnection networks is the hypercube due to its structural regularity, potential…

Complex networks are pervasive in the real world, capturing dyadic interactions between pairs of vertices, and a large corpus has emerged on their mining and modeling. However, many phenomena are comprised of polyadic interactions between…

In this paper we study flag codes of maximum distance. We characterize these codes in terms of, at most, two relevant constant dimension codes naturally associated to them. We do this first for general flag codes and then particularize to…

Partitioning a graph using graph separators, and particularly clique separators, are well-known techniques to decompose a graph into smaller units which can be treated independently. It was previously known that the treewidth was bounded…

We give a method of constructing self-orthogonal codes from equitable partitions of association schemes. By applying this method we construct self-orthogonal codes from some distance-regular graphs. Some of the obtained codes are optimal.…

Some linear codes associated to maximal algebraic curves via Feng-Rao construction are investigated. In several case, these codes have better minimum distance with respect to the previously known linear codes with same length and dimension.

We propose a generative model of temporally-evolving hypergraphs in which hyperedges form via noisy copying of previous hyperedges. Our proposed model reproduces several stylized facts from many empirical hypergraphs, is learnable from…

The Weisfeiler-Leman procedure is a widely-used technique for graph isomorphism testing that works by iteratively computing an isomorphism-invariant coloring of vertex tuples. Meanwhile, a fundamental tool in structural graph theory, which…

We prove improved bounds on how localized an eigenvector of a high girth regular graph can be, and present examples showing that these bounds are close to sharp. This study was initiated by Brooks and Lindenstrauss (2009) who relied on the…

Bilayer graphene (BLG) with a tunable bandgap appears interesting as an alternative to graphene for practical applications, thus its transport properties are being actively pursued. Using density functional theory and perturbation analysis,…

Due to the recent challenges in post-quantum cryptography, several new approaches for code-based cryptography have been proposed. For example, a variant of the McEliece cryptosystem based on interleaved codes was proposed. In order to deem…