Related papers: Classification of linear codes using canonical aug…
In this paper we generalize the canonical positive scaling of rows and columns of a matrix to the scaling of selected-rank subtensors of an arbitrary tensor. We expect our results and framework will prove useful for sparse-tensor completion…
We study the symmetric tensor rank of multiplication over finite field extensions using linearized polynomials. Via field trace, symmetric linearized polynomials are identified with symmetric bilinear forms and symmetric matrices, allowing…
We prove that there exists an algorithm for determining whether two piecewise-linear spatial graphs are isomorphic. In its most general form, our theorem applies to spatial graphs furnished with vertex colorings, edge colorings and/or edge…
We present RandomizedCCA, a randomized algorithm for computing canonical analysis, suitable for large datasets stored either out of core or on a distributed file system. Accurate results can be obtained in as few as two data passes, which…
Recently, linear codes constructed by defining sets have attracted a lot of study, and many optimal linear codes with a few weights have been produced. The objective of this paper is to present a class of binary linear codes with three…
Algorithmic classifications of research publications can be used to study many different aspects of the science system, such as the organization of science into fields, the growth of fields, interdisciplinarity, and emerging topics. How to…
We investigate algorithms for canonical labelling of site graphs, i.e. graphs in which edges bind vertices on sites with locally unique names. We first show that the problem of canonical labelling of site graphs reduces to the problem of…
We describe an algorithm for listing all elements of bounded height in a given number field.
A classification algorithm, called the Linear Centralization Classifier (LCC), is introduced. The algorithm seeks to find a transformation that best maps instances from the feature space to a space where they concentrate towards the center…
We exhibit an explicit, deterministic algorithm for finding a canonical form for a positive definite matrix under unimodular integral transformations. We use characteristic sets of short vectors and partition-backtracking graph software.…
A common approach for studying a solid solution or disordered system within a periodic ab-initio framework is to create a supercell in which a certain amount of target elements is substituted with other ones. The key to generating…
In this paper we describe an algorithm for the computation of canonical forms of finite subsets of $\mathbb{Z}^d$, up to affinities over $\mathbb{Z}$. For fixed dimension $d$, this algorithm has worst-case asymptotic complexity $O(n \log^2…
We provide a combinatorial construction for linear codes attaining the maximum possible number of distinct weights. We then introduce the related problem of determining the existence of linear codes with an arbitrary number of distinct…
This paper examines linear binary codes capable of correcting one or more errors. For the single-error-correcting case, it is shown that the Hamming bound is achieved by a constructive method, and an exact expression for the minimal…
Recently, it was shown that a binary linear code can be associated to a binomial ideal given as the sum of a toric ideal and a non-prime ideal. Since then two different generalizations have been provided which coincide for the binary case.…
A new construction of codes from old ones is considered, it is an extension of the matrix-product construction. Several linear codes that improve the parameters of the known ones are presented.
Canonical matrices of (a) bilinear and sesquilinear forms, (b) pairs of forms, in which every form is symmetric or skew-symmetric, and (c) pairs of Hermitian forms are given over finite fields of characteristic not 2 and over finite…
Tensor expression simplification is an "ancient" topic in computer algebra, a representative of which is the canonicalization of Riemann tensor polynomials. Practically fast algorithms exist for monoterm canonicalization, but not for…
We propose an algorithm to find a lower bound for the number of cyclic codes over any finite field with any given exponent. Besides, we give a formula to find the exponent of BCH codes.
In this paper, we investigate polycyclic codes associated with a trinomial of arbitrary degree $n$ over a finite chain ring $ R.$ We extend the concepts of $ n $-isometry and $ n $-equivalence known for constacyclic codes to this class of…