相关论文: On the minimality of Hamming compatible metrics

A finite set of quantum observables (positive operator valued measures) is called compatible if these observables are marginals of a some observable, called a joint observable of them. For a given set of compatible observables, their joint…

We revisit a fundamental problem in string matching: given a pattern of length m and a text of length n, both over an alphabet of size $\sigma$, compute the Hamming distance between the pattern and the text at every location. Several…

This article investigates the probabilistic relationship between quantum classification of Boolean functions and their Hamming distance. By integrating concepts from quantum computing, information theory, and combinatorics, we explore how…

The Gap-Hamming distance problem is the promise problem of deciding if the Hamming distance $h$ between two strings of length $n$ is greater than $a$ or less than $b$, where the gap $g=|a-b|\geq 1$ and $a$ and $b$ could depend on $n$. In…

A common criterion in the design of finite Hilbert space frames is minimal coherence, as this leads to error reduction in various signal processing applications. Frames that achieve minimal coherence relative to all unit-norm frames are…

When approximating binary similarity using the hamming distance between short binary hashes, we show that even if the similarity is symmetric, we can have shorter and more accurate hashes by using two distinct code maps. I.e. by…

Dubickas and Smyth defined the metric Mahler measure on the multiplicative group of non-zero algebraic numbers. The definition involves taking an infimum over representations of an algebraic number $\alpha$ by other algebraic numbers. We…

We prove that a generically regular semisimple Higgs bundle equipped with a non-degenerate symmetric pairing on any Riemann surface always has a harmonic metric compatible with the pairing. We also study the classification of such…

A physical metric is defined as one which gives a measurable speed of light throughout the whole space time continuum. It will be shown that a metric which satisfies the condition that speed of light on the spherical direction is that in a…

We present a new general method for performing basic arithmetic in the finite field~$\mathbb{F}_p$ for any prime $p>2$ by using traditional binary operations over~$\mathbb{F}_2$. Our new approach is efficient and competitive with current…

A subset of vertices in a graph is called resolving when the geodesic distances to those vertices uniquely distinguish every vertex in the graph. Here, we characterize the resolvability of Hamming graphs in terms of a constrained linear…

Due to the ever rising importance of the network paradigm across several areas of science, comparing and classifying graphs represent essential steps in the networks analysis of complex systems. Both tasks have been recently tackled via…

Let $\mathfrak{M}$ be a class of metric spaces. A metric space $Y$ is minimal $\mathfrak{M}$-universal if every $X\in\mathfrak{M}$ can be isometrically embedded in $Y$ but there are no proper subsets of $Y$ satisfying this property. We find…

The most common decision criteria for decoding are maximum likelihood decoding and nearest neighbor decoding. It is well-known that maximum likelihood decoding coincides with nearest neighbor decoding with respect to the Hamming metric on…

Generating functions for the size of a $r$-sphere, with respect to the Manhattan distance in an $n$-dimensional grid, are used to provide explicit formulas for the minimum and maximum size of an $r$-ball centered at a point of the grid.…

With increasing use of digital control it is natural to view control inputs and outputs as stochastic processes assuming values over finite alphabets rather than in a Euclidean space. As control over networks becomes increasingly common,…

The $r$-th generalized Hamming metric and the $b$-symbol metric are two different generalizations of Hamming metric. The former is used on the wire-tap channel of Type II, and the latter is motivated by the limitations of the reading…

Random probabilities are a key component to many nonparametric methods in Statistics and Machine Learning. To quantify comparisons between different laws of random probabilities several works are starting to use the elegant Wasserstein over…

S-metric and b-metric spaces are metrizable, but it is still quite impossible to get an explicit form of the concerned metric function. To overcome this, the notion of $\phi$-metric is developed by making a suitable modification in triangle…

Previous studies have used a specific success metric within an algorithmic search framework to prove machine learning impossibility results. However, this specific success metric prevents us from applying these results on other forms of…