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A large family of linear codes with flexible parameters from almost bent functions and perfect nonlinear functions are constructed and their parameters are determined. Some constructed linear codes and their related codes are optimal in the…

Abstract separation systems are a new unifying framework in which separations of graph, matroids and other combinatorial structures can be expressed and studied. We characterize the abstract separation systems that have representations as…

We present the notion of separable game with respect to a forward directed hypergraph (FDH-graph), which refines and generalizes that of graphical game. First, we show that there exists a minimal FDH-graph with respect to which a game is…

Hash tables are one of the most fundamental data structures for effectively storing and accessing sparse data, with widespread usage in domains ranging from computer graphics to machine learning. This study surveys the state-of-the-art…

Concurrent hash tables are one of the most important concurrent data structures with numerous applications. Since hash table accesses can dominate the execution time of the overall application, we need implementations that achieve good…

An infinite family of nonschurian separable association schemes is constructed.

Similarity-preserving hashing is a widely-used method for nearest neighbour search in large-scale image retrieval tasks. For most existing hashing methods, an image is first encoded as a vector of hand-engineering visual features, followed…

A directed hypergraph (dihypergraph) consists of a set of vertices and a set of hyperarcs, where each hyperarc is partitioned into a head and a tail. Directed hypergraphs are useful in many applications, including the study of chemical…

Currently known secondary construction techniques for linear codes mainly include puncturing, shortening, and extending. In this paper, we propose a novel method for the secondary construction of linear codes based on their weight…

In this paper we show how to construct new convolutional codes from old ones by applying the well-known techniques: puncturing, extending, expanding, direct sum, the (u|u + v) construction and the product code construction. By applying…

This paper develops a basic theory of H-groups. We introduce a special quotient of H-groups and extend some algebraic constructions of topological groups to the category of H-groups and H-maps. We use these constructions to prove some…

Percolation theory investigates systems of interconnected units, their resilience to damage and their propensity to propagation. For random networks we can solve the percolation problems analytically using the generating function formalism.…

We study the family of intersection graphs of low density objects in low dimensional Euclidean space. This family is quite general, and includes planar graphs. We prove that such graphs have small separators. Next, we present efficient…

Graph clustering is a fundamental problem in unsupervised learning, with numerous applications in computer science and in analysing real-world data. In many real-world applications, we find that the clusters have a significant high-level…

A hypergraph is said to be $1$-Sperner if for every two hyperedges the smallest of their two set differences is of size one. We present several applications of $1$-Sperner hypergraphs and their structure to graphs. In particular, we…

In this paper, we give a new class of reconstructible graphs, which is an extension of my paper `A class of reconstructible graphs'.

Nonstandard graphs have been defined and examined in prior works. The present work does the same for nonstandard digraphs. Since digraphs have more structure than do graphs, the present discussion requires more complicated definitions and…

A family $\mathcal{F}$ of permutations of the vertices of a hypergraph $H$ is called 'pairwise suitable' for $H$ if, for every pair of disjoint edges in $H$, there exists a permutation in $\mathcal{F}$ in which all the vertices in one edge…

In the recent paper entitled "Explicit constructions of MDS self-dual codes" accepted in { IEEE Transactions on Information Theory}, doi: 10.1109/TIT.2019.2954877, the author has constructed families of MDS self-dual codes from genus zero…

We provide a general framework for computing lower-bounds on the sample complexity of recovering the underlying graphs of Ising models, given i.i.d samples. While there have been recent results for specific graph classes, these involve…