Codes and Rings

Theory and Practice

Minjia Shi, Adel Alahmadi, Patrick Solé

• Publisher: Academic Press
• Year: 2017
• Print ISBN: 9780128133880
• eBook ISBN: 9780128133910
• Topic: Mathematics
• Subtopic: Economic Theory
• Index: Mathematics

Codes and Rings: Theory and Practice is a systematic review of literature that focuses on codes over rings and rings acting on codes. Since the breakthrough works on quaternary codes in the 1990s, two decades of research have moved the field far beyond its original periphery. This book fills this gap by consolidating results scattered in the literature, addressing classical as well as applied aspects of rings and coding theory. New research covered by the book encompasses skew cyclic codes, decomposition theory of quasi-cyclic codes and related codes and duality over Frobenius rings. Primarily suitable for ring theorists at PhD level engaged in application research and coding theorists interested in algebraic foundations, the work is also valuable to computational scientists and working cryptologists in the area. - Consolidates 20+ years of research in one volume, helping researchers save time in the evaluation of disparate literature - Discusses duality formulas in the context of Frobenius rings - Reviews decomposition of quasi-cyclic codes under ring action - Evaluates the ideal and modular structure of skew-cyclic codes - Supports applications in data compression, distributed storage, network coding, cryptography and across error-correction

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Foreword
• Introduction
• Chapter 1: Motivation
• Chapter 2: Rings
• Chapter 3: Distances
• Chapter 4: Few Weight Codes
• Chapter 5: Linear Codes
• Chapter 6: Self-dual Codes
• Chapter 7: Cyclic Codes
• Chapter 8: Quasicyclic Codes
• Chapter 9: Quasitwisted Codes
• Chapter 10: Generalized Quasicyclic Codes
• Chapter 11: Skew Cyclic Codes
• Chapter 12: MDR Codes
• Chapter 13: Convolutional Codes
• Chapter 14: Character Sums
• Index