Название: Perfect Codes and Related Structures
Автор: Tuvi Etzion
Издательство: World Scientific Publishing
Год: 2022
Страниц: 436
Язык: английский
Формат: pdf (true), epub
Размер: 18.49 MB
In this monograph, we develop the theory of one of the most fascinating topics in coding theory, namely, perfect codes and related structures. Perfect codes are considered to be the most beautiful structure in coding theory, at least from the mathematical side. These codes are the largest ones with their given parameters. The book develops the theory of these codes in various metrics — Hamming, Johnson, Lee, Grassmann, as well as in other spaces and metrics. It also covers other related structures such as diameter perfect codes, quasi-perfect codes, mixed codes, tilings, combinatorial designs, and more. The goal is to give the aspects of all these codes, to derive bounds on their sizes, and present various constructions for these codes. The intention is to offer a different perspective for the area of perfect codes. Information theory, launched by the pioneering work of Shannon, has generated a lot of applications and ten of thousands of research papers. One can easily say, without stretching the truth, that its influence on our daily lives is pervasive. Coding theory, which is one of the important sub-areas of information theory, started with the work of Golay and Hamming.