Related papers: Three Combinatorial Perspectives on Minimal Codes
We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes…
Combinatorial $t$-designs have nice applications in coding theory, finite geometries and several engineering areas. There are two major methods of constructing $t$-designs. One of them is via group actions of certain permutation groups…
Finding inclusion-minimal "hitting sets" for a given collection of sets is a fundamental combinatorial problem with applications in domains as diverse as Boolean algebra, computational biology, and data mining. Much of the algorithmic…
In this work, we aim to advance the development of a fractal theory for sets of integers. The core idea is to utilize the fractal structure of $p$-adic integers, where $p$ is a prime number, and compare this with conventional densities and…
This work provides an algebraic framework for source coding with decoder side information and its dual problem, channel coding with encoder side information, showing that nested concatenated codes can achieve the corresponding…
We survey recent (and not so recent) results concerning arrangements of lines, points and other geometric objects and the applications these results have in theoretical computer science and combinatorics. The three main types of problems we…
The {\sc $c$-Balanced Separator} problem is a graph-partitioning problem in which given a graph $G$, one aims to find a cut of minimum size such that both the sides of the cut have at least $cn$ vertices. In this paper, we present new…
In this paper we study a family of discrete configuration spaces, the so-called protocol complexes, which are of utmost importance in theoretical distributed computing. Specifically, we consider questions of the existance of compliant…
Codes considered as structures within unit schemes greatly extends the availability of linear block and convolutional codes and allows the construction of these codes to required length, rate, distance and type. Properties of a code emanate…
This paper is intended to provide an introduction to cut elimination which is accessible to a broad mathematical audience. Gentzen's cut elimination theorem is not as well known as it deserves to be, and it is tied to a lot of interesting…
Linear error-correcting codes can be used for constructing secret sharing schemes; however finding in general the access structures of these secret sharing schemes and, in particular, determining efficient access structures is difficult.…
The work in this article is concerned with two different types of families of finite sets: separating families and splitting families (they are also called "systems"). These families have applications in combinatorial search, coding theory,…
Combinatorial designs are closely related to linear codes. In recent year, there are a lot of $t$-designs constructed from certain linear codes. In this paper, we aim to construct $2$-designs from binary three-weight codes. For any binary…
We provide a combinatorial construction for linear codes attaining the maximum possible number of distinct weights. We then introduce the related problem of determining the existence of linear codes with an arbitrary number of distinct…
We study the rigidity of body-and-cad frameworks which capture the majority of the geometric constraints used in 3D mechanical engineering CAD software. We present a combinatorial characterization of the generic minimal rigidity of a subset…
Robust Optimization is becoming increasingly important in machine learning applications. This paper studies the problem of robust submodular minimization subject to combinatorial constraints. Constrained Submodular Minimization arises in…
We study the convergence of distributions on finite paths of weighted digraphs, namely the family of Boltzmann distributions and the sequence of uniform distributions. Targeting applications to the convergence of distributions on paths, we…
We consider the problem of constructing deletion correcting codes over a binary alphabet and take a graph theoretic view. An $n$-bit $s$-deletion correcting code is an independent set in a particular graph. We propose constructing such a…
For general connections, the problem of finding network codes and optimizing resources for those codes is intrinsically difficult and little is known about its complexity. Most of the existing solutions rely on very restricted classes of…
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…