Related papers: Galois Field Arithmetics for Linear Network Coding…
Low-rank parity-check (LRPC) are rank-metric codes over finite fields, which have been proposed by Gaborit et al. (2013) for cryptographic applications. Inspired by a recent adaption of Gabidulin codes to certain finite rings by Kamche et…
We study scalar-linear and vector-linear solutions of the generalized combination network. We derive new upper and lower bounds on the maximum number of nodes in the middle layer, depending on the network parameters and the alphabet size.…
Linear codes over finite rings become one of hot topics in coding theory after Hommons et al.([4], 1994) discovered that several remarkable nonlinear binary codes with some linear-like properties are the images of Gray map of linear codes…
The performance of graph programs depends highly on the algorithm, the size and structure of the input graphs, as well as the features of the underlying hardware. No single set of optimizations or one hardware platform works well across all…
Achieving high-performance GPU kernels requires optimizing algorithm implementations to the targeted GPU architecture. It is of utmost importance to fully use the compute and memory hierarchy, as well as available specialised hardware.…
Existing construction algorithms of block network-error correcting codes require a rather large field size, which grows with the size of the network and the number of sinks, and thereby can be prohibitive in large networks. In this work, we…
Coded Distributed Matrix Multiplication (CDMM) is a distributed matrix multiplication (DMM) for large-scale matrices through a coding scheme such that any $R$ worker node among all $N$ worker nodes can recover the final product, where $N$…
Graph neural networks have been used for a variety of learning tasks, such as link prediction, node classification, and node clustering. Among them, link prediction is a relatively under-studied graph learning task, with current…
The problem of coding for networks experiencing worst-case symbol errors is considered. We argue that this is a reasonable model for highly dynamic wireless network transmissions. We demonstrate that in this setup prior network…
Error control is significant to network coding, since when unchecked, errors greatly deteriorate the throughput gains of network coding and seriously undermine both reliability and security of data. Two families of codes, subspace and rank…
Let $\ell\geq 5$ be a prime number and $\mathbb{F}_\ell$ denote the finite field with $\ell$ elements. We show that the number of Galois extensions of the rationals with Galois group isomorphic to $GL_2(\mathbb{F}_\ell)$ and absolute…
Hypergraphs offer flexible and robust data representations for many applications, but methods that work directly on hypergraphs are not readily available and tend to be prohibitively expensive. Much of the current analysis of hypergraphs…
The rapid progression in wireless communication technologies, especially in multicarrier code-division multiple access (MC-CDMA), there is a need of advanced code construction methods. Traditional approaches, mainly based on generalized…
We study a class of linear network coding (LNC) schemes, called circular-shift LNC, whose encoding operations consist of only circular-shifts and bit-wise additions (XOR). Formulated as a special vector linear code over GF($2$), an…
The rate of a network code is the ratio of the block size of the network's messages to that of its edge codewords. We compare the linear capacities and achievable rate regions of networks using finite field alphabets to the more general…
Cheng and Wan have related the decoding of Reed-Solomon codes to the computation of discrete logarithms over finite fields, with the aim of proving the hardness of their decoding. In this work, we experiment with solving the discrete…
Structural parameters are normally extracted from observed galaxies by fitting analytic light profiles to the observations. Obtaining accurate fits to high-resolution images is a computationally expensive task, requiring many model…
We develop a Galois descent approach to finite-field Fourier spectra over an arbitrary finite base field. Let $\mathbb K=\mathbb F_q$ and $\mathbb L=\mathbb F_{q^m}$. If a Fourier transform is applied to a $\mathbb K$-valued vector, then…
Recently, several approaches have emerged for generating neural representations with multiple levels of detail (LODs). LODs can improve the rendering by using lower resolutions and smaller model sizes when appropriate. However, existing…
Linear network coding transmits information in terms of a basis of a vector space and the information is received as a basis of a possible altered vectorspace. Ralf Koetter and Frank R. Kschischang in Coding for errors and erasures in…