Related papers: Linear Programming Bounds
Locally repairable codes (LRCs) are a class of codes designed for the local correction of erasures. They have received considerable attention in recent years due to their applications in distributed storage. Most existing results on LRCs do…
In this thesis we present several results in coding theory, concerning error-correcting codes and the Shannon capacity. 1. We give a general symmetry reduction of matrices occuring in semidefinite programs in coding theory. 2. We apply the…
Computer programming (coding) is indispensable for researchers across disciplines, yet it remains challenging to learn and time-consuming to carry out. Generative AI, particularly large language models (LLMs), has the potential to transform…
Function-correcting codes (FCCs) protect specific function evaluations of a message against errors. This condition imposes a less stringent distance requirement than classical error-correcting codes (ECCs), allowing for reduced redundancy.…
Low Rank Parity Check (LRPC) codes form a class of rank-metric error-correcting codes that was purposely introduced to design public-key encryption schemes. An LRPC code is defined from a parity check matrix whose entries belong to a…
Large Language Model (LLM) based coding tools have been tremendously successful as software development assistants, yet they are often designed for general purpose programming tasks and perform poorly for more specialized domains such as…
We consider linear network error correction (LNEC) coding when errors may occur on edges of a communication network of which the topology is known. In this paper, we first revisit and explore the framework of LNEC coding, and then unify two…
The locally repairable code (LRC) studied in this paper is an $[n,k]$ linear code of which the value at each coordinate can be recovered by a linear combination of at most $r$ other coordinates. The central problem in this work is to…
This book provides an introduction to the mathematical analysis of deep learning. It covers fundamental results in approximation theory, optimization theory, and statistical learning theory, which are the three main pillars of deep neural…
We define two extensions of the typed linear lambda-calculus that yield minimal Turing-complete systems. The extensions are based on unbounded recursion in one case, and bounded recursion with minimisation in the other. We show that both…
In this paper we describe our experience in developing curriculum courses aimed at graduate students in emerging computational fields, including biology and medical science. We focus primarily on computational data analysis and statistical…
This article is intended as a guide for new graduate students in the field of computational science. With the increasing influx of students from diverse backgrounds joining the ever-popular field, this short guide aims to help students…
This book is about dynamic programming and its applications in economics, finance, and adjacent fields. It brings together recent innovations in the theory of dynamic programming and provides applications and code that can help readers…
This survey describes probabilistic algorithms for linear algebra computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problem instances. The paper…
Large Language Models (LLMs) have demonstrated remarkable capabilities across a variety of software engineering and coding tasks. However, their application in the domain of code and compiler optimization remains underexplored. Training…
Understanding the relationship between data compression and the capabilities of Large Language Models (LLMs) is crucial, especially in specialized domains like code intelligence. Prior work posited a linear relationship between compression…
This paper focuses on Code Generation task that aims at generating relevant code fragments according to given natural language descriptions. In the process of software development, developers often encounter two scenarios. One is requested…
Code summary generation is the task of writing natural language descriptions of a section of source code. Recent advances in Large Language Models (LLMs) and other AI-based technologies have helped make automatic code summarization a…
Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable…
We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes…