A nice expository account of some of these issues is:
Thomas M. Thomson, From Error-Correcting Codes Through Sphere Packings to Simple Groups, published by MAA, 1983.
There is also the book by Sloane and Conway:
http://web.archive.org/web/20130420140222/http://www2.research.att.com/~njas/doc/splag.htmlhttp://neilsloane.com/doc/splag.html
entitled: Sphere Packings, Lattices, and Groups.