Related papers: Rank-Metric Codes and Their Applications
We consider the decoding problem or the problem of finding low weight codewords for rank metric codes. We show how additional information about the codeword we want to find under the form of certain linear combinations of the entries of the…
Codes are widely used in many engineering applications to offer robustness against noise. In large-scale systems there are several types of noise that can affect the performance of distributed machine learning algorithms -- straggler nodes,…
A subspace of matrices over $\mathbb{F}_{q^e}^{m\times n}$ can be naturally embedded as a subspace of matrices in $\mathbb{F}_q^{em\times en}$ with the property that the rank of any of its matrix is a multiple of $e$. It is quite natural to…
This book has four chapters. In chapter one we just recall the notion of RD codes, MRD codes, circulant rank codes and constant rank codes and describe their properties. In chapter two we introduce few new classes of codes and study some of…
We study information leakage in secure linear network coding schemes based on nested rank-metric codes. We show that the amount of information leaked to an adversary that observes a subset of network links is characterized by the…
Image ranking is to rank images based on some known ranked images. In this paper, we propose an improved linear ordinal distance metric learning approach based on the linear distance metric learning model. By decomposing the distance metric…
In this paper, a Roos like bound on the minimum distance for skew cyclic codes over a general field is provided. The result holds in the Hamming metric and in the rank metric. The proofs involve arithmetic properties of skew polynomials and…
Sum-rank-metric codes have wide applications in the multishot network coding and the distributed storage. Linearized Reed-Solomon codes, sum-rank BCH codes and their Welch-Berlekamp type decoding algorithms were proposed and studied. They…
Hashing, or learning binary embeddings of data, is frequently used in nearest neighbor retrieval. In this paper, we develop learning to rank formulations for hashing, aimed at directly optimizing ranking-based evaluation metrics such as…
Matrix multiplication is a fundamental building block for large scale computations arising in various applications, including machine learning. There has been significant recent interest in using coding to speed up distributed matrix…
The MacWilliams identity, which relates the weight distribution of a code to the weight distribution of its dual code, is useful in determining the weight distribution of codes. In this paper, we derive the MacWilliams identity for linear…
We study the rank weight hierarchy, thus in particular the rank metric, of cyclic codes over the finite field $\mathbb F_{q^m}$, $q$ a prime power, $m \geq 2$. We establish the rank weight hierarchy for $[n,n-1]$ cyclic codes and…
Maximum Hermitian rank metric codes were introduced by Schmidt in 2018 and in this paper we propose both interpolation-based encoding and decoding algorithms for this family of codes when the length and the minimum distance of the code are…
We investigate the distance properties of linear locally recoverable codes (LRC codes) with all-symbol locality and availability. New upper and lower bounds on the minimum distance of such codes are derived. The upper bound is based on the…
The link prediction task on knowledge graphs without explicit negative triples in the training data motivates the usage of rank-based metrics. Here, we review existing rank-based metrics and propose desiderata for improved metrics to…
Reed-Solomon codes and Gabidulin codes have maximum Hamming distance and maximum rank distance, respectively. A general construction using skew polynomials, called skew Reed-Solomon codes, has already been introduced in the literature. In…
The matrices of spanning rooted forests are studied as a tool for analysing the structure of networks and measuring their properties. The problems of revealing the basic bicomponents, measuring vertex proximity, and ranking from preference…
The problem of frequent pattern mining has been studied quite extensively for various types of data, including sets, sequences, and graphs. Somewhat surprisingly, another important type of data, namely rank data, has received very little…
This paper presents and analyzes a novel concatenated coding scheme for enabling error resilience in two distributed storage settings: one being storage using existing regenerating codes and the second being storage using locally repairable…
As distributed systems increase in size, the need for scalable algorithms becomes more and more important. We argue that in the context of system identification, an essential building block of any scalable algorithm is the ability to…