
From Error-Correcting Codes Through Sphere Packings to Simple Groups
Thomas M. Thompson(Author)
Mathematical Association of America (MAA) (Publisher)
Published on 14. October 2004
Book
Paperback/Softback
244 pages
978-0-88385-037-4 (ISBN)
Description
This book traces a remarkable path of mathematical connections through seemingly disparate topics.
More details
Language
English
Place of publication
Washington DC
United States
Product notice
Paperback (trade)
Unsewn / adhesive bound
Dimensions
Height: 188 mm
Width: 126 mm
Thickness: 15 mm
Weight
236 gr
ISBN-13
978-0-88385-037-4 (9780883850374)
Schweitzer Classification
Content
1. The origin of error-correcting codes; an introduction to coding; the work of Hamming; the Hamming-Holbrook patent; the Hamming codes are linear; the work of Golay; the priority controversy; 2. From coding to sphere packing; an introduction to sphere packing; the Leech connection; the origin of Leech's first packing in E24; the matrix for Leech's first packing; the Leech lattice; 3. From sphere packing to new simple groups; is there an interesting group in Leech's lattice?; the hard sell of a simple group; twelve hours on Saturday, six on Wednesday; the structure of 0; 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 ?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; Bibliography; Index.