Perfect Codes And Related Structures is popular PDF and ePub book, written by Tuvi Etzion in 2022-03-14, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Perfect Codes And Related Structures can be Read Online from any device for your convenience.
Perfect Codes And Related Structures Book PDF Summary
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. For example, in many chapters there is a section devoted to diameter perfect codes. In these codes, anticodes are used instead of balls and these anticodes are related to intersecting families, an area that is part of extremal combinatorics. This is one example that shows how we direct our exposition in this book to both researchers in coding theory and mathematicians interested in combinatorics and extremal combinatorics. New perspectives for MDS codes, different from the classic ones, which lead to new directions of research on these codes are another example of how this book may appeal to both researchers in coding theory and mathematicians.The book can also be used as a textbook, either on basic course in combinatorial coding theory, or as an advance course in combinatorial coding theory.
Detail Book of Perfect Codes And Related Structures PDF
- Author : Tuvi Etzion
- Release : 14 March 2022
- Publisher : World Scientific
- ISBN : 9789811255892
- Genre : Mathematics
- Total Page : 436 pages
- Language : English
- PDF File Size : 17,6 Mb
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