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Recently, a new method for encoding data sets in the form of "Density Codes" was proposed in the literature (Courrieu, 2006). This method allows to compare sets of points belonging to every multidimensional space, and to build shape spaces…
We investigate CSS and CSS-T quantum error-correcting codes from the point of view of their existence, rarity, and performance. We give a lower bound on the number of pairs of linear codes that give rise to a CSS code with good correction…
Guruswami and Xing introduced subspace designs in 2013 to give the first construction of positive rate rank metric codes list-decodable beyond half the distance. In this paper we provide bounds involving the parameters of a subspace design,…
In this work, we provide a way of constructing new semiorthogonal decompositions using metric techniques (\`a la Neeman). Given a semiorthogonal decomposition on a category with a special kind of metric, which we call a compressible metric,…
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…
The setting of projective systems can be used to study the parameters of a projective linear code $\mathcal{C}$. This can be done by considering the intersections of the point set $\Omega$ defined by the columns of a generating matrix for…
In constraint programming and related paradigms, a modeller specifies their problem in a modelling language for a solver to search and return its solution(s). Using high-level modelling languages such as Essence, a modeller may express…
We present an iterative algorithm for computing an invariant subspace associated with the algebraically smallest eigenvalues of a large sparse or structured Hermitian matrix A. We are interested in the case in which the dimension of the…
Deep ensemble is a simple yet powerful way to improve the performance of deep neural networks. Under this motivation, recent works on mode connectivity have shown that parameters of ensembles are connected by low-loss subspaces, and one can…
High-dimensional multivariate time series are challenging due to the dependent and high-dimensional nature of the data, but in many applications there is additional structure that can be exploited to reduce computing time along with…
One-point codes on the Hermitian curve produce long codes with excellent parameters. Feng and Rao introduced a modified construction that improves the parameters while still using one-point divisors. A separate improvement of the parameters…
One of the main problems of the research area of network coding is to compute good lower and upper bounds of the achievable cardinality of so-called subspace codes in $\operatorname{PG}(n,q)$, i.e., the set of subspaces of $\mathbb{F}_q^n$,…
Construction of subspace codes with good parameters is one of the most important problems in random network coding. In this paper we present first a generalization of the concept of cyclic subspaces codes and further we show that the usual…
In this paper, we propose a sufficient condition for a family of 2-generator self-orthogonal quasi-cyclic codes with respect to Hermitian inner product. Supported in the Hermitian construction, we show algebraic constructions of good…
We are concerned with the problem of designing large families of subsets over a common labeled ground set that have small pairwise intersections and the property that the maximum discrepancy of the label values within each of the sets is…
Scientific fields such as insider-threat detection and highway-safety planning often lack sufficient amounts of time-series data to estimate statistical models for the purpose of scientific discovery. Moreover, the available limited data…
This work considers the convergence of GMRES for non-singular problems. GMRES is interpreted as the GCR method which allows for simple proofs of the convergence estimates. Preconditioning and weighted norms within GMRES are considered. The…
In the near future, the $5^{th}$ generation (5G) wireless systems will be established. They will consist of an integration of different techniques, including distributed antenna systems and massive multiple-input multiple-output systems,…
One of the main objectives of quantum error-correction theory is to construct quantum codes with optimal parameters and properties. In this paper, we propose a class of 2-generator quasi-cyclic codes and study their applications in the…
We present a new efficient algortithm for construction of linear latent structure (LLS) models. This algorithm reduces a problem of estimation of model parameters to a sequence of problems of linear algebra, which assures a low…