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Book Cover
Author Thompson, Thomas M., author.

Title From error-correcting codes through sphere packings to simple groups / by Thomas M. Thompson
Published [Washington] : Mathematical Association of America, ©1983


Description 1 online resource (xiv, 228 pages) : illustrations
Series The Carus mathematical monographs ; no. 21
Carus mathematical monographs ; no. 21.
Contents The origin of error-correcting codes -- From coding to sphere packing -- From sphere packing to new simple groups -- Appendix 1. Densest known sphere packings -- Appendix 2. Further properties of the (12, 24) Golay code and the related Steiner system S(5, 8, 24) -- Appendix 3. A calculation of the number of spheres with centers in [lambda]₂ adjacent to one, two, three and four adjacent spheres with centers in [lambda]₂ -- Appendix 4. The Mathieu group M₂₄ and the order of M₂₂ -- Appendix 5. The proof of Lemma 3.3 -- Appendix 6. The sporadic simple groups
Summary This book traces a remarkable path of mathematical connections through seemingly disparate topics. Frustrations with a 1940's electro-mechanical computer at a premier research laboratory begin this story. Subsequent mathematical methods of encoding messages to ensure correctness when transmitted over noisy channels led to discoveries of extremely efficient lattice packings of equal-radius balls, especially in 24-dimensional space. In turn, this highly symmetric lattice, with each point neighbouring exactly 196,560 other points, suggested the possible presence of new simple groups as groups of symmetries. Indeed, new groups were found and are now part of the 'Enormous Theorem' - the classification of all simple groups whose entire proof runs to some 10,000+ pages. And these connections, along with the fascinating history and the proof of the simplicity of one of those 'sporadic' simple groups, are presented at an undergraduate mathematical level. --
Bibliography Includes bibliographical references (pages 217-223) and index
Notes Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. MiAaHDL
digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL
Print version record
Subject Error-correcting codes (Information theory)
Finite simple groups.
Finite simple groups
MATHEMATICS -- Algebra -- Intermediate.
Error-correcting codes (Information theory)
Finite simple groups
Einfache Gruppe
Group theory.
Coding theory.
Codes correcteurs d'erreurs (théorie de l'information)
Groupes simples finis.
Form Electronic book
ISBN 9781614440215