Let n; k; d; q]-codes be linear codes of length n, dimension k and minimum Hamming distance d over GF (q). In this paper, eighteen codes are constructed which improve the known lower bounds on minimum distance.

We prove that the space of persistence diagrams on $n$ points (with bottleneck or a Wasserstein distance) coarsely embeds into Hilbert by showing it is asymptotic dimension $2n$. Such an embedding enables utilisation techniques diagrams. also when number not bounded, corresponding spaces do have finite dimension. Furthermore, in case distance, does embed space.

Figure 1. Vertical dimension recorder. Rectangular plate (1) with central hollow cylinder. Rod (2). Short hollow cylinder (3) with hook. Light plastic 20-cm ruler (4) with hole in its upper end. Square plate with adjustable needle pointer (5). The Glossary of Prosthodontic Terms defines the physiologic rest position (PRP) as “the mandibular position assumed when the head is in an upright positi...

In order to cope with the exponential time complexity of graph edit distance, several polynomial-time approximation algorithms have been proposed in recent years. The Hausdorff edit distance is a quadratic-time matching procedure for labeled graphs which reduces the edit distance to a correspondence problem between local substructures. In its original formulation, nodes and their adjacent edges...

We present shortest path maps that support min-link queries from any source point on a line segment to destination points in either a simple polygon or a polygonal domain (a polygon with holes). These structures are more versatile than the traditional shortest path map from a fixed source point, and we use them to compute the min-link Fréchet distance between two polygonal curves. In addition t...

In computer vision, the partial Hausdorff distances (PHDs) are used to compare images but with strong limitations of using fixed fractions. In this paper, we formulate an adaptive and robust Hausdorff distance (ARHD) with nonparametric and robust statistical methods. The new distance is estimated using the empirical distribution of the distance variable based on the distance map of the template...

The Reeb graph is a construction that studies a topological space through the lens of a real valued function. It has been commonly used in applications, however its use on real data means that it is desirable and increasingly necessary to have methods for comparison of Reeb graphs. Recently, several metrics on the set of Reeb graphs have been proposed. In this paper, we focus on two: the functi...

An important code of length n is obtained by taking centralizer of a square matrix over a finite field Fq. Twisted centralizer codes, twisted by an element a ∈ Fq, are also similar type of codes but different in nature. The main results were embedded on dimension and minimum distance. In this paper, we have defined a new family of twisted centralizer codes namely generalized twisted centralizer...