Description 
1 online resource (xiv, 228 pages) : illustrations 
Series 
The Carus mathematical monographs ; no. 21 

Carus mathematical monographs ; no. 21.

Contents 
The origin of errorcorrecting 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 electromechanical 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 equalradius balls, especially in 24dimensional 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.  Amazon.com 
Bibliography 
Includes bibliographical references (pages 217223) 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. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL 

digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL 

Print version record 
Subject 
Errorcorrecting codes (Information theory)


Finite simple groups.


Finite simple groups


MATHEMATICS  Algebra  Intermediate.


Errorcorrecting codes (Information theory)


Finite simple groups


Einfache Gruppe


Fehlerkorrekturcode


Geschichte


Kugelpackung


ALGEBRA.


ERROR CORRECTING.


COMBINATORIAL ANALYSIS.


GROUP THEORY.


HISTORIES.


Group theory.


Coding theory.


Codes correcteurs d'erreurs (théorie de l'information)


Groupes simples finis.

Form 
Electronic book

ISBN 
9781614440215 

1614440212 
