相关论文: Spectral approach to linear programming bounds on …

Coded computing is a distributed paradigm that uses coding theory to introduce \textit{redundancy} and overcome bottlenecks in large-scale systems. In the same vein, randomized numerical linear algebra employs probabilistic methods to…

Connectivity problems like k-Path and k-Disjoint Paths relate to many important milestones in parameterized complexity, namely the Graph Minors Project, color coding, and the recent development of techniques for obtaining kernelization…

In this paper, we develop a new decoding algorithm of a binary linear codes for symbol-pair read channels. Symbol-pair read channel has recently been introduced by Cassuto and Blaum to model channels with high write resolution but low read…

An infinite set is orbit-finite if, up to permutations of the underlying structure of atoms, it has only finitely many elements. We study a generalisation of linear programming where constraints are expressed by an orbit-finite system of…

We continue the study of the linear programming bounds for sphere packing introduced by Cohn and Elkies. We use theta series to give another proof of the principal theorem, and present some related results and conjectures.

Let $A(n,d)$ (respectively $A(n,d,w)$) be the maximum possible number of codewords in a binary code (respectively binary constant-weight $w$ code) of length $n$ and minimum Hamming distance at least $d$. By adding new linear constraints to…

Exploring the power of linear programming for combinatorial optimization problems has been recently receiving renewed attention after a series of breakthrough impossibility results. From an algorithmic perspective, the related questions…

A fundamental problem in quantum coding theory is to determine the maximum size of quantum codes of given block length and distance. A recent work introduced bounds based on semidefinite programming, strengthening the well-known quantum…

Historically, scalability has been a major challenge to the successful application of semidefinite programming in fields such as machine learning, control, and robotics. In this paper, we survey recent approaches for addressing this…

Codes in finite projective spaces equipped with the subspace distance have been proposed for error control in random linear network coding. Here we collect the present knowledge on lower and upper bounds for binary subspace codes for…

Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the possible violation of a restriction. Each risk constraint induces an uncertainty set of coefficients,…

We algebraically compute all possible sectional curvature values for canonical algebraic curvature tensors, and use this result to give a method for constructing general sectional curvature bounds. We use a well-known method to…

We study asymptotic lower and upper bounds for the sizes of constant dimension codes with respect to the subspace or injection distance, which is used in random linear network coding. In this context we review known upper bounds and show…

A fertile area of recent research has demonstrated concrete polynomial time lower bounds for solving natural hard problems on restricted computational models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path, Mod6-SAT,…

We develop a new method for studying the asymptotics of symmetric polynomials of representation-theoretic origin as the number of variables tends to infinity. Several applications of our method are presented: We prove a number of theorems…

A well studied problem in algebraic complexity theory is the determination of the complexity of problems relying on evaluations of bilinear maps. One measure of the complexity of a bilinear map (or 3-tensor) is the optimal number of…

Linear operator broadcast channel (LOBC) models the scenario of multi-rate packet broadcasting over a network, when random network coding is applied. This paper presents the framework of algebraic coding for LOBCs and provides a…

In this paper q-ary Raptor codes under ML decoding are considered. An upper bound on the probability of decoding failure is derived using the weight enumerator of the outer code, or its expected weight enumerator if the outer code is drawn…

We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite…

The paper introduces new bounds on the asymptotic density of parity-check matrices and the achievable rates under ML decoding of binary linear block codes transmitted over memoryless binary-input output-symmetric channels. The lower bounds…