Related papers: Algorithms for Computing the Free Distance of Conv…
The distance of a classical or quantum code is a key figure of merit which reflects its capacity to detect errors. Quantum LDPC code families have considerable promise in reducing the overhead required for fault-tolerant quantum…
The distance distribution of a code is the vector whose $i^\text{th}$ entry is the number of pairs of codewords with distance $i$. We investigate the structure of the distance distribution for cyclic orbit codes, which are subspace codes…
A general method for constructing convolutional codes from units in Laurent series over matrix rings is presented. Using group ring as matrix rings, this forms a basis for in-depth exploration of convolutional codes from group ring…
It is known that maximum distance separable and maximum distance profile convolutional codes exist over large enough finite fields of any characteristic for all parameters $(n,k,\delta)$. It has been conjectured that the same is true for…
We provide a simple method and relevant theoretical analysis for efficiently estimating higher-order lp distances. While the analysis mainly focuses on l4, our methodology extends naturally to p = 6,8,10..., (i.e., when p is even).…
The article provides a survey on convolutional codes stressing the connections to module theory and systems theory. Constructions of codes with maximal possible distance and distance profile are provided. The article will appear as book…
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…
Maximum distance profile (MDP) convolutional codes have the property that their column distances are as large as possible. It has been shown that, transmitting over an erasure channel, these codes have optimal recovery rate for windows of a…
A systematic convolutional encoder of rate $(n-1)/n$ and maximum degree $D$ generates a code of free distance at most ${\cal D} = D+2$ and, at best, a column distance profile (CDP) of $[2,3,\ldots,{\cal D}]$. A code is \emph{Maximum…
The decoding of error syndromes of surface codes with classical algorithms may slow down quantum computation. To overcome this problem it is possible to implement decoding algorithms based on artificial neural networks. This work reports a…
In this paper the characterization as convolution operators of filters sending finite energy signals to bounded signals is used to prove several theoretical results concerning the distance between the ideal filter and the spaces of…
We outline a method to estimate the value of computation for a flexible algorithm using empirical data. To determine a reasonable trade-off between cost and value, we build an empirical model of the value obtained through computation, and…
The distance of a stabilizer quantum code is a very important feature since it determines the number of errors that can be detected and corrected. We present three new fast algorithms and implementations for computing the symplectic…
Distance transformation is an image processing technique used for many different applications. Related to a binary image, the general idea is to determine the distance of all background points to the nearest object point (or vice versa). In…
Approximating distance is one of the key challenge in a facility location problem. Several algorithms have been proposed, however, none of them focused on estimating distance between two concave regions. In this work, we present an…
In evolutionary optimization, it is important to understand how fast evolutionary algorithms converge to the optimum per generation, or their convergence rate. This paper proposes a new measure of the convergence rate, called average…
In this paper, we employ the linear systems representation of a convolutional code to develop a decoding algorithm for convolutional codes over the erasure channel. We study the decoding problem using the state space description and this…
A spread code is a set of vector spaces of a fixed dimension over a finite field Fq with certain properties used for random network coding. It can be constructed in different ways which lead to different decoding algorithms. In this work we…
Convolutional codes with a maximum distance profile attain the largest possible column distances for the maximum number of time instants and thus have outstanding error-correcting capability especially for streaming applications. Explicit…
It has been known that the distribution of the random distances between two uniformly distributed points within a convex polygon can be obtained based on its chord length distribution (CLD). In this report, we first verify the existing…