Related papers: Computer classification of linear codes
Computationally efficient classification system architecture is proposed. It utilizes fast tensor-vector multiplication algorithm to apply linear operators upon input signals . The approach is applicable to wide variety of recognition…
Systems of linear equations are used to model a wide array of problems in all fields of science and engineering. Recently, it has been shown that quantum computers could solve linear systems exponentially faster than classical computers,…
These notes are inspired by the theory of cellular automata. A linear cellular automaton on a lattice of finite rank or on a toric grid is a discrete dinamical system generated by a convolution operator with kernel concentrated in the…
In this paper, we give a survey of the known results concerning the tensor rank of the multiplication in finite extensions of finite fields, enriched with some not published recent results as well as analyzes enhancing the qualitative…
Linear codes have been an interesting topic in both theory and practice for many years. In this paper, for an odd prime power $q$, we construct some class of linear code over finite field $\mathbb{F}_q$ with defining set be the preimage of…
We propose a new class of space-time block codes based on finite-field rank-metric codes in combination with a rank-metric-preserving mapping to the set of Eisenstein integers. It is shown that these codes achieve maximum diversity order…
The set of nonnegative integer lattice points in a polytope, also known as the fiber of a linear map, makes an appearance in several applications including optimization and statistics. We address the problem of sampling from this set using…
Interior-point algorithms constitute a very interesting class of algorithms for solving linear-programming problems. In this paper we study efficient implementations of such algorithms for solving the linear program that appears in the…
In this paper, we give quantum algorithms for two fundamental computation problems: solving polynomial systems over finite fields and optimization where the arguments of the objective function and constraints take values from a finite field…
We exhibit a probabilistic algorithm which computes a rational point of an absolutely irreducible variety over a finite field defined by a reduced regular sequence. Its time--space complexity is roughly quadratic in the logarithm of the…
This paper develops two heuristic algorithms to solve graph isomorphism, using free energy encoding. The first algorithm uses four types of encoding refinement techniques such that every graph can be distinguished by a canonical number…
The intrinsic structure of binary fields poses a challenging complexity problem from both hardware and software point of view. Motivated by applications to modern cryptography, we describe some simple techniques aimed at performing…
In this note, we study the classification of $\mathbb{Z}_4$-codes. For some special cases $(k_1,k_2)$, by hand, we give a classification of $\mathbb{Z}_4$-codes of length $n$ and type $4^{k_1}2^{k_2}$ satisfying a certain condition. Our…
There has been a recent push in making machine learning models more interpretable so that their performance can be trusted. Although successful, these methods have mostly focused on the deep learning methods while the fundamental…
In this paper, we propose a linear complexity encoding method for arbitrary LDPC codes. We start from a simple graph-based encoding method ``label-and-decide.'' We prove that the ``label-and-decide'' method is applicable to Tanner graphs…
The linear programming method is applied to the space $\U_n(\C)$ of unitary matrices in order to obtain bounds for codes relative to the diversity sum and the diversity product. Theoretical and numerical results improving previously known…
Algorithmic approach to the problem of linearization by point transformation of ordinary differential equation of arbitrary order is presented. Test-linearization is purely algorithmic.
In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be…
This paper evaluates algorithms for classification and outlier detection accuracies in temporal data. We focus on algorithms that train and classify rapidly and can be used for systems that need to incorporate new data regularly. Hence, we…
We exploit a prescription to observe directly the physical properties of the thermodynamic limit under continuously applied field in one-dimensional quantum finite lattice systems. By systematically scaling down the energy of the…