Ebook: From error-correcting codes through sphere packings to simple groups

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 LAMBDA2; 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