Related papers: Linear Programming Bounds
We apply the semidefinite programming method to derive bounds for projective codes over a finite field.
Binary code analysis plays a pivotal role in various software security applications, such as software maintenance, malware detection, software vulnerability discovery, patch analysis, etc. However, unlike source code, understanding binary…
In this Macaulay2 \cite{M2} package we define an object called {\it linear code}. We implement functions that compute basic parameters and objects associated with a linear code, such as generator and parity check matrices, the dual code,…
This volume contains a selection of papers presented at Linearity/TLLA 2018: Joint Linearity and TLLA workshops (part of FLOC 2018) held on July 7-8, 2018 in Oxford. Linearity has been a key feature in several lines of research in both…
Programmers increasingly rely on Large Language Models (LLMs) for code generation. However, misalignment between programmers' goals and generated code complicates the code evaluation process and demands frequent switching between prompt…
A systematic literature review is a research process that identifies, evaluates, and interprets all relevant study findings connected to specific research questions, topics, or phenomena of interest. In this work, a thorough review of the…
This Survey provides an overview of techniques in termination analysis for programs with numerical variables and transitions defined by linear constraints. This subarea of program analysis is challenging due to the existence of undecidable…
Linear programming is the seminal optimization problem that has spawned and grown into today's rich and diverse optimization modeling and algorithmic landscape. This article provides an overview of the recent development of first-order…
Function-correcting codes were introduced in the work "Function-Correcting Codes" (FCC) by Lenz et al. 2023, which provides a graphical representation for the problem of constructing function-correcting codes. We use this function dependent…
Understanding binary code is an essential but complex software engineering task for reverse engineering, malware analysis, and compiler optimization. Unlike source code, binary code has limited semantic information, which makes it…
We propose several improvements for Linear Programming (LP) decoding algorithms for High Density Parity Check (HDPC) codes. First, we use the automorphism groups of a code to create parity check matrix diversity and to generate valid cuts…
In this book, there are five chapters: Systems of Linear Equations, Vector Spaces, Homogeneous Systems, Characteristic Equation of Matrix, and Matrix Dot Product. It has also exercises at the end of each chapter above to let students…
We describe a new parameterized family of symmetric error-correcting codes with low-density parity-check matrices (LDPC). Our codes can be described in two seemingly different ways. First, in relation to Reed-Muller codes: our codes are…
The material in this book is presented to graduate students in Information and Communication theory. The idea is that we give an introduction to particular applications of information theory and coding in digital communications. The goal is…
Large language models (LLMs) for code have become indispensable in various domains, including code generation, reasoning tasks and agent systems. While open-access code LLMs are increasingly approaching the performance levels of proprietary…
The rapid proliferation of diverse programming languages presents both opportunities and challenges for developing multilingual code LLMs. While existing techniques often train code LLMs by simply aggregating multilingual code data, few…
The increasing complexity of software systems has driven significant advancements in program analysis, as traditional methods unable to meet the demands of modern software development. To address these limitations, deep learning techniques,…
In recent years, end-to-end Large Language Model (LLM) technology has shown substantial advantages across various domains. As critical system software and infrastructure, compilers are responsible for transforming source code into target…
We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented, including sparse PSD cuts, and…
This is a draft of the textbook/monograph that presents computability theory using string diagrams. The introductory chapters have been taught as graduate and undergraduate courses and evolved through 8 years of lecture notes. The later…