Related papers: Binary Fields on Limited Systems
Binary neural networks (BNNs) are an attractive solution for developing and deploying deep neural network (DNN)-based applications in resource constrained devices. Despite their success, BNNs still suffer from a fixed and limited…
Binary embedding of high-dimensional data aims to produce low-dimensional binary codes while preserving discriminative power. State-of-the-art methods often suffer from high computation and storage costs. We present a simple and fast…
Inpainting-based compression represents images in terms of a sparse subset of its pixel data. Storing the carefully optimised positions of known data creates a lossless compression problem on sparse and often scattered binary images. This…
Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are…
This paper considers the task of performing binary search under noisy decisions, focusing on the application of target area localization. In the presence of noise, the classical partitioning approach of binary search is prone to error…
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…
The works presented in this habilitation concern the algorithmics of polynomials. This is a central topic in computer algebra, with numerous applications both within and outside the field - cryptography, error-correcting codes, etc. For…
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…
The quadratic unconstrained binary optimization (QUBO) problem arises in diverse optimization applications ranging from Ising spin problems to classical problems in graph theory and binary discrete optimization. The use of preprocessing to…
The paper introduces a new technique for compressing Binary Decision Diagrams in those cases where random access is not required. Using this technique, compression and decompression can be done in linear time in the size of the BDD and…
This paper describes a new method of data encoding which may be used in various modern digital, computer and telecommunication systems and devices. The method permits the compression of data for storage or transmission, allowing the exact…
Kernel methods are considered an effective technique for on-line learning. Many approaches have been developed for compactly representing the dual solution of a kernel method when the problem imposes memory constraints. However, in…
The article contents suggestions on how to perform the Fast Fourier Transform over Large Finite Fields. The technique is to use the fact that the multiplicative groups of specific prime fields are surprisingly composite.
Multiple-input multiple-output (MIMO) systems are playing an increasing and interesting role in the recent wireless communication. The complexity and the performance of the systems are driving the different studies and researches. Lattices…
We study the complexity of cutting planes and branching schemes from a theoretical point of view. We give some rigorous underpinnings to the empirically observed phenomenon that combining cutting planes and branching into a branch-and-cut…
For the past decades, linear codes with few weights have been widely studied, since they have applications in space communications, data storage and cryptography. In this paper, a class of binary linear codes is constructed and their weight…
Binary embedding is a nonlinear dimension reduction methodology where high dimensional data are embedded into the Hamming cube while preserving the structure of the original space. Specifically, for an arbitrary $N$ distinct points in…
A representation of finite fields that has proved useful when implementing finite field arithmetic in hardware is based on an isomorphism between subrings and fields. In this paper, we present an unified formulation for multiplication in…
There are several methods for constructing secret sharing schemes, one of which is based on coding theory. Theoretically, every linear code can be used to construct secret sharing schemes. However, in general, determining the access…
The present paper deals with the discrete inverse problem of reconstructing binary matrices from their row and column sums under additional constraints on the number and pattern of entries in specified minors. While the classical…