Related papers: On the Linear Programming Bound for Lee-codes
We consider linear network error correction (LNEC) coding when errors may occur on edges of a communication network of which the topology is known. In this paper, we first revisit and explore the framework of LNEC coding, and then unify two…
In this note we develop a linear programming framework to produce upper and lower bounds for the lonely runner problem.
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…
Ahlswede and Katona (1977) posed the following isodiametric problem in Hamming spaces: For every $n$ and $1\le M\le2^{n}$, determine the minimum average Hamming distance of binary codes with length $n$ and size $M$. Fu, Wei, and Yeung…
We design a heuristic method, a genetic algorithm, for the computation of an upper bound of the minimum distance of a linear code over a finite field. By the use of the row reduced echelon form, we obtain a permutation encoding of the…
Whereas many results are known about thresholds for ensembles of low-density parity-check codes under message-passing iterative decoding, this is not the case for linear programming decoding. Towards closing this knowledge gap, this paper…
Linear computation coding is concerned with the compression of multidimensional linear functions, i.e. with reducing the computational effort of multiplying an arbitrary vector to an arbitrary, but known, constant matrix. This paper…
New lower bounds on the minimum average Hamming distance of binary codes are derived. The bounds are obtained using linear programming approach.
Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…
In this paper we present an extension of known semidefinite and linear programming upper bounds for spherical codes and consider a version of this bound for distance graphs. We apply the main result for the distance distribution of a…
Linear programming (LP) decoding approximates maximum-likelihood (ML) decoding of a linear block code by relaxing the equivalent ML integer programming (IP) problem into a more easily solved LP problem. The LP problem is defined by a set of…
Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…
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…
We define a metric on $\mathbb{F}_q^n$ using the linear complexity of finite sequences. We will then develop a coding theory for this metric. We will give a Singleton-like bound and we will give constructions of subspaces of…
We consider $t$-Lee-error-correcting codes of length $n$ over the residue ring $\mathbb{Z}_m := \mathbb{Z}/m\mathbb{Z}$ and determine upper and lower bounds on the number of $t$-Lee-error-correcting codes. We use two different methods,…
A major issue of locally repairable codes is their robustness. If a local repair group is not able to perform the repair process, this will result in increasing the repair cost. Therefore, it is critical for a locally repairable code to…
The minimum distance is one of the most important combinatorial characterizations of a code. The maximum likelihood decoding problem is one of the most important algorithmic problems of a code. While these problems are known to be hard for…
We consider linear codes over a field in which the error values are restricted to a subgroup of its unit group. This scenario captures Lee distance codes as well as codes over the Gaussian or Eisenstein integers. Codes correcting restricted…
We present a bound on the size of linear codes. This bound is independent of other known bounds, e.g. the Griesmer bound.
Codes over permutations under the infinity norm have been recently suggested as a coding scheme for correcting limited-magnitude errors in the rank modulation scheme. Given such a code, we show that a simple relabeling operation, which…