Related papers: Linear Programming Bounds
Random linear codes are a workhorse in coding theory, and are used to show the existence of codes with the best known or even near-optimal trade-offs in many noise models. However, they have little structure besides linearity, and are not…
This book provides a broad overview of Natural Language Generation (NLG), including technology, user requirements, evaluation, and real-world applications. The focus is on concepts and insights which hopefully will remain relevant for many…
Our title challenges the reader to venture beyond linear algebra in designing models and in thinking about numerical algorithms for identifying solutions. This article accompanies the author's lecture at the International Congress of…
Coding, which targets compressing and reconstructing data, and intelligence, often regarded at an abstract computational level as being centered around model learning and prediction, interweave recently to give birth to a series of…
We propose using natural language outlines as a novel modality and interaction surface for providing AI assistance to developers throughout the software development process. An NL outline for a code function comprises multiple statements…
Generative AI models, specifically large language models (LLMs), have made strides towards the long-standing goal of text-to-code generation. This progress has invited numerous studies of user interaction. However, less is known about the…
Predictive coding offers a potentially unifying account of cortical function -- postulating that the core function of the brain is to minimize prediction errors with respect to a generative model of the world. The theory is closely related…
Locally repairable codes (LRCs) are error correcting codes used in distributed data storage. Besides a global level, they enable errors to be corrected locally, reducing the need for communication between storage nodes. There is a close…
We present the theory of linear rank-metric codes from the point of view of their fundamental parameters. These are: the minimum rank distance, the rank distribution, the maximum rank, the covering radius, and the field size. The focus of…
This is a survey on the use of low-degree polynomials to predict and explain the apparent statistical-computational tradeoffs in a variety of average-case computational problems. In a nutshell, this framework measures the complexity of a…
This paper provides a comprehensive survey on recent advances in deep learning (DL) techniques for the channel coding problems. Inspired by the recent successes of DL in a variety of research domains, its applications to the physical layer…
R. W. Hamming published the Hamming codes and the sphere packing bound in 1950. In the past 75 years, infinite families of distance-optimal linear codes over finite fields with minimum distance at most 8 with respect to the sphere packing…
Artificial intelligence has recently experienced remarkable advances, fueled by large models, vast datasets, accelerated hardware, and, last but not least, the transformative power of differentiable programming. This new programming…
Many important quantities of interest are only partially identified from observable data: the data can limit them to a set of plausible values, but not uniquely determine them. This paper develops a unified framework for covariate-assisted…
How can complexity theory and algorithms benefit from practical advances in computing? We give a short overview of some prior work using practical computing to attack problems in computational complexity and algorithms, informally describe…
We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite…
The main objective of this paper is to extend the previously defined code family over the ring $\mathfrak{R}=\sum\limits_{s=0}^{4} v_{5}^{s} \mathcal{A}_{4}$ to $\mathfrak{R}^{s,m}=\sum\limits_{\varsigma=1}^{m}…
In the 2017 paper by Dougherty, Kim, Ozkaya, Sok, and Sol\'e about the linear programming bound for LCD codes the notion $\mathrm{LCD}[n,k]$ was defined for binary LCD $[n,k]$-codes. We find the formula for $\mathrm{LCD}[n,2]$.
Neural Code Intelligence -- leveraging deep learning to understand, generate, and optimize code -- holds immense potential for transformative impacts on the whole society. Bridging the gap between Natural Language and Programming Language,…
Mathematical programming is a branch of applied mathematics and has recently been used to derive new decoding approaches, challenging established but often heuristic algorithms based on iterative message passing. Concepts from mathematical…