From Error-Correcting Codes through Sphere Packings to Simple Groups.

Abstract

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.