3
$\begingroup$

I am a college freshmen currently enrolled in a second semester of abstract algebra and a course on error correcting codes. I've read about the Leech Lattice online, and I'd be very interested in learning about it and its connection to sporadic groups and Golay code. Are there any books/resources about it that I would be able to understand, and if not, are there any prerequisites I should learn first?

Thanks!

$\endgroup$
1
  • $\begingroup$ In addition to the suggestions in Will Jagy's answer, you might have a look at Sphere Packings, Lattices, and Groups, which is a little bit scattershot but very readable and talks about both the Leech Lattice and many of its cousins. $\endgroup$ Feb 24, 2017 at 3:55

1 Answer 1

5
$\begingroup$

start with Thompson's book. Then Ebeling on lattices, which helped me a good deal. Let me look up full titles

Thomas M. Thompson, From Error Correcting Codes through Sphere Packings to Simple Groups

Wolfgang Ebeling, Lattices and Codes there is now a third edition

Well, why not. A technique that was probably invented by Conway shows that any "even" lattice with covering radius strictly below $\sqrt 2$ has class number one. G. Nebe first published a list of these, maximum dimension possible is ten (goes back to G. L. Watson). I and Pete Clark published a small correction by finding lattices with class number one. Meanwhile, the Leech lattice has covering radius exactly $\sqrt 2,$ and class number $24.$ The thing about the covering radius is that one may draw pictures for the two dimensional case, on ordinary graph paper, and learn a good deal.

$\endgroup$
1
  • $\begingroup$ Thanks! I bought the book, it seems excellent so far. $\endgroup$ Mar 4, 2017 at 8:13

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .