From Error-Correcting Codes Through Sphere Packings to Simple Groups, Volume 21

Front Cover
Cambridge University Press, 1983 - Language Arts & Disciplines - 228 pages
0 Reviews
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.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

The Origin of ErrorCorrecting Codes
1
From Coding to Sphere Packing
61
From Sphere Packing to New Simple Groups
109
Densest Known Sphere Packings
176
Further Properties of the 1224 Golay
187
A Calculation of the Number of Spheres
193
The Mathieu Group M24 and the Order
197
The Proof of Lemma 3 3
209
Bibliography
217
Index
225
Copyright

Common terms and phrases

References to this book

All Book Search results »

Bibliographic information