Related papers: Endomorphisms of Linear Block Codes
It is well known that a set of non-defect matrices can be simultaneously diagonalized if and only if the matrices commute. In the case of non-commuting matrices, the best that can be achieved is simultaneous block diagonalization. Here we…
Large language models (LLMs) achieve remarkable generative performance, yet their output quality is dependent on the decoding strategy. While sampling-based methods (e.g., top-k, nucleus) and search-and-select based methods (e.g., beam…
Automorphism-ensemble decoding is applied to the Plotkin constituents of Reed-Muller codes, resulting in a new soft-decision decoding algorithm with state-of-the-art performance versus complexity trade-offs.
The aim of this work is to study the structure and properties of the binary LCD codes having an automorphisms of odd prime order and to present a method for their construction.
In this work, we introduce a framework to study the effect of random operations on the combinatorial list-decodability of a code. The operations we consider correspond to row and column operations on the matrix obtained from the code by…
Over a decade ago, it was demonstrated that quantum computing has the potential to revolutionize numerical linear algebra by enabling algorithms with complexity superior to what is classically achievable, e.g., the seminal HHL algorithm for…
Automated medical coding, an essential task for healthcare operation and delivery, makes unstructured data manageable by predicting medical codes from clinical documents. Recent advances in deep learning and natural language processing have…
In computational anatomy, the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework has become a central tool for modeling smooth, invertible transformations between shapes such as curves or landmarks. In this paper, we extend…
Mitigating errors in computing and communication systems has seen a great deal of research since the beginning of the widespread use of these technologies. However, as we develop new methods to do computation or communication, we also need…
Autoencoders are effective deep learning models that can function as generative models and learn latent representations for downstream tasks. The use of graph autoencoders - with both encoder and decoder implemented as message passing…
The purpose of this paper is to present the structure of the linear codes over a finite field with q elements that have a permutation automorphism of order m. These codes can be considered as generalized quasi-cyclic codes. Quasi-cyclic…
The order statistics based list decoding techniques for linear binary block codes of small to medium block length are investigated. The construction of the list of the test error patterns is considered. The original order statistics…
Hinging on ideas from physical-layer network coding, some promising proposals of coded random access systems seek to improve system performance (while preserving low complexity) by means of packet repetitions and decoding of linear…
This paper introduces a description of Endomorphisms of the translation group in an affine plane, will define the addition and composition of the set of endomorphisms and specify the neutral elements associated with these two actions and…
In recent years, the rise of deep learning and automation requirements in the software industry has elevated Intelligent Software Engineering to new heights. The number of approaches and applications in code understanding is growing, with…
Low-density parity-check (LDPC) convolutional codes are capable of achieving excellent performance with low encoding and decoding complexity. In this paper we discuss several graph-cover-based methods for deriving families of time-invariant…
This work introduces a decoding strategy for binary self-dual codes possessing an automorphism of a specific type. The proposed algorithm is a hard decision iterative decoding scheme. The enclosed experiments show that the new decoding…
The encoding of solutions in black-box optimization is a delicate, handcrafted balance between expressiveness and domain knowledge -- between exploring a wide variety of solutions, and ensuring that those solutions are useful. Our main…
Spectral Embedding (SE) has often been used to map data points from non-linear manifolds to linear subspaces for the purpose of classification and clustering. Despite significant advantages, the subspace structure of data in the original…
Let $d, n \in \mathbb{Z}^+$ such that $1\leq d \leq n$. A $d$-code $\mathcal{C} \subset \mathbb{F}_q^{n \times n}$ is a subset of order $n$ square matrices with the property that for all pairs of distinct elements in $\mathcal{C}$, the rank…