Perfect Codes And Related Structures

This book develops the theory of perfect codes and related structures, including Hamming, Johnson, Lee, Grassmann, and other spaces and metrics. It covers other related structures such as diameter perfect codes, quasi-perfect codes, mixed codes, tiling, combinatorial designs, and more. It offers new perspectives for MDS codes and can be used as a textbook for basic and advance courses in combinatorial coding theory.

Format: Hardback
Length: 436 pages
Publication date: 12 April 2022
Publisher: World Scientific Publishing Co Pte Ltd

In this comprehensive monograph, we delve into the fascinating realm of perfect codes and related structures, which are widely regarded as the epitome of beauty in coding theory, particularly from a mathematical perspective. These codes stand out as the largest ones with their specified parameters, showcasing remarkable elegance and efficiency. The book comprehensively develops the theory of perfect codes across various metrics, including Hamming, Johnson, Lee, Grassmann, and other spaces and metrics. It also explores other related structures such as diameter perfect codes, quasi-perfect codes, mixed codes, tiling, combinatorial designs, and more.

Our primary objective is to provide a comprehensive overview of these codes, derive bounds on their sizes, and present diverse constructions for them. By offering a different perspective on the field of perfect codes, we aim to appeal to both researchers in coding theory and mathematicians with an interest in combinatorics and extremal combinatorics.

Throughout the book, we explore various chapters dedicated to diameter perfect codes. In these codes, anticodes replace balls, and they are closely linked to intersecting families, a branch of extremal combinatorics. This example illustrates how we tailor our exposition to cater to both coding theory experts and mathematicians passionate about combinatorics and extremal combinatorics.

Furthermore, the book presents new perspectives for MDS codes, diverging from the traditional approaches, which open up fresh avenues for research in this area. These novel insights can captivate both coding theory researchers and mathematicians with an affinity for combinatorial coding theory.

Moreover, this book serves as an invaluable textbook, suitable for both introductory and advanced courses in combinatorial coding theory. It provides a solid foundation for understanding the principles and applications of perfect codes, making it an essential resource for students and scholars alike.

In conclusion, this monograph offers a deep and comprehensive exploration of perfect codes and related structures, providing a fresh perspective on this captivating field. Whether you are a coding theory researcher or a mathematician interested in combinatorics and extremal combinatorics, this book is a valuable resource that will enhance your understanding and contribute to your intellectual growth.

Weight: 778g
Dimension: 159 x 236 x 31 (mm)
ISBN-13: 9789811255878