Related papers: Decoding Downset codes over a finite grid
In this paper, we introduce a new family of codes relevent for rank and sum-rank metrics. These codes are based on an effective Chinese remainders theorem for linearized polynomials over finite fields. We propose a decoding algorithm for…
In this paper, we describe how to get Janet decomposition for a finite set of terms and detect completeness of that set by means of the associated Bar Code. Moreover, we explain an algorithm to find a variable ordering (if it exists) s.t. a…
In the literature, several different identification problems in graphs have been studied, the most widely studied such problems are the ones based on dominating sets as a tool of identification. Hereby, the objective is to separate any two…
We present a construction of subspace codes along with an efficient algorithm for list decoding from both insertions and deletions, handling an information-theoretically maximum fraction of these with polynomially small rate. Our…
We present a novel global compression framework for deep neural networks that automatically analyzes each layer to identify the optimal per-layer compression ratio, while simultaneously achieving the desired overall compression. Our…
Compared with classical block codes, efficient list decoding of rank-metric codes seems more difficult. Although the list decodability of random rank-metric codes and limits to list decodability have been completely determined, little work…
The extended Euclidean algorithm (EEA) for polynomial greatest common divisors is commonly used in solving the key equation in the decoding of Reed-Solomon (RS) codes, and more generally in BCH decoding. For this particular application, the…
We present a new upper bound for the orders of derivatives in the Rosenfeld-Groebner algorithm. This algorithm computes a regular decomposition of a radical differential ideal in the ring of differential polynomials over a differential…
We introduce the concepts of complex Grassmannian codes and designs. Let G(m,n) denote the set of m-dimensional subspaces of C^n: then a code is a finite subset of G(m,n) in which few distances occur, while a design is a finite subset of…
While feasibility and obtaining a solution of a given network coding problem are well studied, the decoding procedure and complexity have not garnered much attention. We consider the decoding problem in a network wherein the sources…
(Hyper)Graph decomposition is a family of problems that aim to break down large (hyper)graphs into smaller sub(hyper)graphs for easier analysis. The importance of this lies in its ability to enable efficient computation on large and complex…
This article is about a decoding algorithm for error-correcting subspace codes. A version of this algorithm was previously described by Rosenthal, Silberstein and Trautmann. The decoding algorithm requires the code to be defined as the…
High-rate concatenated quantum codes offer a promising pathway toward fault-tolerant quantum computation, yet designing efficient decoders that fully exploit their error-correction capability remains a significant challenge. In this work,…
It has been discovered that linear codes may be described by binomial ideals. This makes it possible to study linear codes by commutative algebra and algebraic geometry methods. In this paper, we give a decoding algorithm for binary linear…
We construct a family of root-finding algorithms which exploit the branched covering structure of a polynomial of degree $d$ with a path-lifting algorithm for finding individual roots. In particular, the family includes an algorithm that…
In many high-impact applications, it is important to ensure the quality of output of a machine learning algorithm as well as its reliability in comparison with the complexity of the algorithm used. In this paper, we have initiated a…
Schubert calculus provides algebraic tools to solve enumerative problems. There have been several applied problems in systems theory, linear algebra and physics which were studied by means of Schubert calculus. The method is most powerful…
Topological subsystem codes can combine the advantages of both topological codes and subsystem codes. Suchara et al. proposed a framework based on hypergraphs for construction of such codes. They also studied the performance of some…
An upper dominating set in a graph is a minimal (with respect to set inclusion) dominating set of maximum cardinality. The problem of finding an upper dominating set is generally NP-hard. We study the complexity of this problem in classes…
Decoding algorithms based on approximate tensor network contraction have proven tremendously successful in decoding 2D local quantum codes such as surface/toric codes and color codes, effectively achieving optimal decoding accuracy. In this…