Related papers: Implementing Basic Arithmetic in $\mathbb{F}_p$ vi…
We study distributed protocols for finding all pairs of similar vectors in a large dataset. Our results pertain to a variety of discrete metrics, and we give concrete instantiations for Hamming distance. In particular, we give improved…
We show that a broad class of $(+,\diamond)$ vector products (for binary integer functions $\diamond$) are equivalent under one-to-polylog reductions to the computation of the Hamming distance. Examples include: the dominance product, the…
We present effective upper bounds on the symmetric bilinear complexity of multiplication in extensions of a base finite field Fp2 of prime square order, obtained by combining estimates on gaps between prime numbers together with an optimal…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
Recent work on approximate linear programming (ALP) techniques for first-order Markov Decision Processes (FOMDPs) represents the value function linearly w.r.t. a set of first-order basis functions and uses linear programming techniques to…
This paper presents a family of new methods for locating/fitting hyperplanes with respect to a given set of points. We introduce a general framework for a family of aggregation criteria of different distance-based errors. The most popular…
Linear error-correcting codes form the mathematical backbone of modern digital communication and storage systems, but identifying champion linear codes (linear codes achieving or exceeding the best known minimum Hamming distance) remains…
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…
Application of the minimum distance method to the linear regression model for estimating regression parameters is a difficult and time-consuming process due to the complexity of its distance function, and hence, it is computationally…
Suppose that we have two similar files stored on different computers. We need to send the file from the first computer to the second one trying to minimize the number of bits transmitted. This article presents a survey of results known for…
In this work, we study linear codes with the folded Hamming distance, or equivalently, codes with the classical Hamming distance that are linear over a subfield. This includes additive codes. We study MDS codes in this setting and define…
In this paper, we propose and study $r$-minimal codes, a natural extension of minimal codes which have been extensively studied with respect to Hamming metric, rank metric and sum-rank metric. We first propose $r$-minimal codes in a general…
This paper establishes a novel upper bound-termed the arithmetic Singleton bound-on the Hamming distance of any simple-root constacyclic code over a finite field. The key technical ingredient is the notion of multiple equal-difference (MED)…
Solving the error correcting code is an important goal with regard to communication theory.To reveal the error correcting code characteristics, several researchers have applied a statistical-mechanical approach to this problem. In our…
The aim of this work is to algebraically describe the relative generalized Hamming weights of evaluation codes. We give a lower bound for these weights in terms of a footprint bound. We prove that this bound can be sharp. We compute the…
Codes are crucial in many areas of applications. Different types of codes are designed to meet specific needs, which makes them more effective and useful. Linear codes are extensively used in data storage systems. Identifying codes are…
Recently, arithmetic coding has attracted the attention of many scholars because of its high compression capability. Accordingly, in this paper a method which adds secrecy to this well-known source code is proposed. Finite state arithmetic…
Independent parallel q-ary symmetric channels are a suitable transmission model for several applications. The proposed weighted-Hamming metric is tailored to this setting and enables optimal decoding performance. We show that some…
We propose a binary message passing decoding algorithm for product codes based on generalized minimum distance decoding (GMDD) of the component codes, where the last stage of the GMDD makes a decision based on the Hamming distance metric.…
The constrained minimization (respectively maximization) of directed distances and of related generalized entropies is a fundamental task in information theory as well as in the adjacent fields of statistics, machine learning, artificial…