Related papers: An Improved Linear Programming Bound on the Averag…
The problem of finding code distance has been long studied for the generic ensembles of linear codes and led to several algorithms that substantially reduce exponential complexity of this task. However, no asymptotic complexity bounds are…
This paper provides new and improved Singleton-like bounds for Lee metric codes over integer residue rings. We derive the bounds using various novel definitions of generalized Lee weights based on different notions of a support of a linear…
Let $f$ be a polynomial in $n$ variables $x_1,\dots,x_n$ with real coefficients. In [Ghasemi-Marshal], Ghasemi and Marshall give an algorithm, based on geometric programming, which computes a lower bound for $f$ on $\mathbb{R}^n$. In…
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…
A linear-programming decoder for \emph{nonbinary} expander codes is presented. It is shown that the proposed decoder has the maximum-likelihood certificate properties. It is also shown that this decoder corrects any pattern of errors of a…
We consider the problem of describing the typical (possibly) non-linear code of minimum distance bounded from below over a large alphabet. We concentrate on block codes with the Hamming metric and on subspace codes with the injection…
In this paper, we exploit linear programming duality in the online setting (i.e., where input arrives on the fly) from the unique perspective of designing lower bounds on the competitive ratio. In particular, we provide a general technique…
The binary asymmetric channel is a model for practical communication systems where the error probabilities for symbol transitions $0\rightarrow 1$ and $1\rightarrow0$ differ substantially. In this paper, we introduce the notion of…
We illustrate how computer-aided methods can be used to investigate the fundamental limits of the caching systems, which are significantly different from the conventional analytical approach usually seen in the information theory…
We construct new linear codes with high minimum distance d. In at least 12 cases these codes improve the minimum distance of the previously known best linear codes for fixed parameters n,k. Among these new codes there is an optimal ternary…
We study distributed protocols for finding all pairs of similar vectors in a large dataset. Our results pertain to a variety of discrete metrics, and we give concrete instantiations for Hamming distance. In particular, we give improved…
Many consensus string problems are based on Hamming distance. We replace Hamming distance by the more flexible (e.g., easily coping with different input string lengths) dynamic time warping distance, best known from applications in time…
The minimum distance graph of a code has the codewords as vertices and edges exactly when the Hamming distance between two codewords equals the minimum distance of the code. A constructive proof for reconstructibility of an extended perfect…
A lower bound on the minimum required code length of binary codes is obtained. The bound is obtained based on observing a close relation between the Ulam's liar game and channel coding. In fact, Spencer's optimal solution to the game is…
Association schemes are central objects in algebraic combinatorics, with the classical schemes lying at their core. These classical association schemes essentially consist of the Hamming and Johnson schemes, and their $q$-analogs: bilinear…
We derive a new estimate of the size of finite sets of points in metric spaces with few distances. The following applications are considered: (1) we improve the Ray-Chaudhuri--Wilson bound of the size of uniform intersecting families of…
In this paper, we study the minimum distances of binary linear codes with parity check matrices formed from subset inclusion matrices $W_{t,n,k}$, representing $t$-element subsets versus $k$-element subsets of an $n$-element set. We provide…
Binary linear codes with good parameters have important applications in secret sharing schemes, authentication codes, association schemes, and consumer electronics and communications. In this paper, we construct several classes of binary…
Feasible binary programs often have multiple optimal solutions, which is of interest in applications as they allow the user to choose between alternative optima without deteriorating the objective function. In this article, we present the…
In this paper, we improve the well-known level-1 weight bound, also known as Chang's lemma, by using an induction method. Our bounds are close to optimal no matter when the set is large or small. Our bounds can be seen as bounds on the…