Related papers: Construction of dyadic MDS matrices for cryptograp…
In inverting large sparse matrices, the key difficulty lies in effectively exploiting sparsity during the inversion process. One well-established strategy is the nested dissection, which seeks the so-called sparse Cholesky factorization. We…
In this paper, we propose two novel modulation concepts based on a simple maximum distance separable (MDS) code { and show that these concepts can achieve better error performance than index modulation (IM) and related schemes.} In the…
The notion of universally decodable matrices (UDMs) was recently introduced by Tavildar and Viswanath while studying slow fading channels. It turns out that the problem of constructing UDMs is tightly connected to the problem of…
Maximum distance separable (MDS) and almost maximum distance separable (AMDS) codes have been widely used in various fields such as communication systems, data storage, and quantum codes because of their algebraic properties and excellent…
We present a set of algorithms implementing multidimensional scaling (MDS) for large data sets. MDS is a family of dimensionality reduction techniques using a $n \times n$ distance matrix as input, where $n$ is the number of individuals,…
In this paper, we propose a new secure distributed matrix multiplication (SDMM) scheme using the inner product partitioning. We construct a scheme with a minimal number of workers and no redundancy, and another scheme with redundancy…
Linear complementary-dual (LCD for short) codes are linear codes that intersect with their duals trivially. LCD codes have been used in certain communication systems. It is recently found that LCD codes can be applied in cryptography. This…
The growing privacy concerns and the communication costs associated with transmitting raw data have resulted in techniques like federated learning, where the machine learning models are trained at the edge nodes, and the parameter updates…
The paper is devoted to the problem of erasure coding in distributed storage. We consider a model of storage that assumes that nodes are organized into equally sized groups, called racks, that within each group the nodes can communicate…
Circulant Maximum Distance Separable (MDS) matrices have gained significant importance due to their applications in the diffusion layer of the AES block cipher. In $2013$, Gupta and Ray established that circulant involutory matrices of…
Masked diffusion language models (MDLMs) have recently emerged as a new paradigm in language modeling, offering flexible generation dynamics and enabling efficient parallel decoding. However, existing decoding strategies for pre-trained…
Machine Learning (ML) is used for developing wall functions for Improved Delayed Detached Eddy Simulations (IDDES). The ML model is based on KDtree which essentially is a fast look-up table. It searches the nearest target datapoint(s) for…
Distributed storage codes have important applications in the design of modern storage systems. In a distributed storage system, every storage node has a probability to fail and once an individual storage node fails, it must be reconstructed…
Multidimensional scaling (MDS) is a popular dimensionality reduction techniques that has been widely used for network visualization and cooperative localization. However, the traditional stress minimization formulation of MDS necessitates…
Masked Diffusion Models (MDMs) offer a promising alternative to autoregressive language models by enabling parallel token generation and bidirectional context modeling. However, their inference speed is significantly limited by the…
Nonnegative matrix factorization (NMF) has attracted much attention in the last decade as a dimension reduction method in many applications. Due to the explosion in the size of data, naturally the samples are collected and stored…
MDS self-dual codes over finite fields have attracted a lot of attention in recent years by their theoretical interests in coding theory and applications in cryptography and combinatorics. In this paper we present a series of MDS self-dual…
Maximum distance separable (MDS) and near maximum distance separable (NMDS) codes have been widely used in various fields such as communication systems, data storage, and quantum codes due to their algebraic properties and excellent…
A theoretical approach is proposed to calculate an effective dielectric constant of a matrix disperse system (MDS) of metallic particles (spheres) randomly distributed and embedded in a uniform dielectric medium. Deviations from the…
In a multi-server system, how can one get better performance than random assignment of jobs to servers if queue-states cannot be queried by the dispatcher? A replication strategy has recently been proposed where $d$ copies of each arriving…