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In this paper, we mainly study quaternary linear codes and their binary subfield codes. First we obtain a general explicit relationship between quaternary linear codes and their binary subfield codes in terms of generator matrices and…
Block full rank pencils introduced in [Dopico et al., Local linearizations of rational matrices with application to rational approximations of nonlinear eigenvalue problems, Linear Algebra Appl., 2020] allow us to obtain local information…
In this paper, the problem of matching pairs of correlated random graphs with multi-valued edge attributes is considered. Graph matching problems of this nature arise in several settings of practical interest including social network…
Low-rank matrix completion addresses the problem of completing a matrix from a certain set of generic specified entries. Over the complex numbers a matrix with a given entry pattern can be uniquely completed to a specific rank, called the…
Linear codes play a central role in coding theory and have applications in several branches of mathematics. For error correction purposes the minimum Hamming distance should be as large as possible. Linear codes related to applications in…
We consider the link prediction problem in a partially observed network, where the objective is to make predictions in the unobserved portion of the network. Many existing methods reduce link prediction to binary classification problem.…
We propose an algorithm for classification of linear codes over different finite fields based on canonical augmentation. We apply this algorithm to obtain classification results over fields with 2, 3 and 4 elements.
Traditional approaches for learning on categorical data underexploit the dependencies between columns (\aka fields) in a dataset because they rely on the embedding of data points driven alone by the classification/regression loss. In…
We study the (in)dependence of additivity and homogeneity conditions in the definition of linear mappings between vector spaces over the same scalar field. Unlike other works on the subject, dealing with particular fields like real or…
Estimating the linear dimensionality of a data set in the presence of noise is a common problem. However, data may also be corrupted by monotone nonlinear distortion that preserves the ordering of matrix entries but causes linear methods…
We introduce a framework for spline spaces of hierarchical type, based on a parent-children relation, which is very convenient for the analysis as well as the implementation of adaptive isogeometric methods. Such framework makes it simple…
We describe a framework for random pairwise comparisons matrices, inspired by selected constructions releted to the so called inconsistency reduction of pairwise comparisons (PC) matrices. In to build up structures on random pairwise…
In this paper, we study the symmetric rank of products of linear forms and an irreducible quadratic form. The main result presents a new, non-trivial lower bound for the rank, and the arguments rely on the apolarity lemma. In the special…
In this short note, we give a new sufficient condition for a linear map from a product of copies of a field to endomorphisms of a finite dimensional vector space over the same field to be an algebra homomorphism. We expect that this result…
For binary $[n,k,d]$ linear locally repairable codes (LRCs), two new upper bounds on $k$ are derived. The first one applies to LRCs with disjoint local repair groups, for general values of $n,d$ and locality $r$, containing some previously…
Every m by n matrix A with rank r has exactly r independent rows and r independent columns. The fact has become the most fundamental theorem in linear algebra such that we may favor it in an unconscious way. The sole aim of this paper is to…
For each natural number $n$, we define a category whose objects are discriminant algebras in rank $n$, i.e. functorial means of attaching to each rank-$n$ algebra a quadratic algebra with the same discriminant. We show that the discriminant…
Construction of phylogenetic trees and networks for extant species from their characters represents one of the key problems in phylogenomics. While solution to this problem is not always uniquely defined and there exist multiple methods for…
Feature selection is an important problem in high-dimensional data analysis and classification. Conventional feature selection approaches focus on detecting the features based on a redundancy criterion using learning and feature searching…
A novel framework is introduced to formalize identifiability in well-specified but ill-posed linear regression models. The framework is distribution-free and accommodates highly correlated features that may or may not relate to the…