Talk:Leech polytope
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What are the coords of Leech?[edit source]
H A M 1 (talk) 03:16, 7 January 2023 (UTC)
- See for yourself. The New Kid (talk) 09:20, 2 April 2023 (UTC)
- leech lattice can be constructed from 3 e8 lattices witch make simpler coords H A M 1 (talk) 19:22, 2 April 2023 (UTC)
- Neat. You want to add the construction, restricted to the 196560 points we care about, in front of the Golay-code approach? Then change the start of my stuff to "The coordinates can also be obtained from the extended binary Golay code."? The New Kid (talk) 06:11, 3 April 2023 (UTC)
- leech lattice coords without using golay code? H A M 1 (talk) 20:07, 5 April 2023 (UTC)
- I don't know if we should delete it. We have multiple coords on oca. But it is true that none of them involve a huge ugly matrix. How simple is this 3 E8 construction? The New Kid (talk) 20:53, 5 April 2023 (UTC)
- leech lattice coords without using golay code? H A M 1 (talk) 20:07, 5 April 2023 (UTC)
- Neat. You want to add the construction, restricted to the 196560 points we care about, in front of the Golay-code approach? Then change the start of my stuff to "The coordinates can also be obtained from the extended binary Golay code."? The New Kid (talk) 06:11, 3 April 2023 (UTC)
- leech lattice can be constructed from 3 e8 lattices witch make simpler coords H A M 1 (talk) 19:22, 2 April 2023 (UTC)
How do you get from the 4096 codewords of the Golay code to the 196560 vertices of the Leech polytope? I can't find any information online on why these are the Leech polytope's vertex coordinates. Plasmath (talk) 15:14, 5 April 2023 (UTC)
- I think it has to do with a classification of all the vectors of minimal norm - that is, the ones closest to the center. In section 3 of this talk, the author finds all the vectors that fit certain restrictions. These restrictions and why they're used (although I'm not sure how to answer this) might make a good transition in our article, between "here's the codewords" and "here's some vertices." The New Kid (talk) 20:49, 5 April 2023 (UTC)
Sources mostly regarding the Miracle Octad Generator[edit source]
Sources I found in case someone wants to add an esoteric and unclear method of construction:
- The Leech lattice Λ and the Conway group ·O revisited
- Error-correction and the binary Golay code]
- The Miracle Octad Generator
- An implementation of Curtis' Miracle Octad Generator...
If, in a paper, you come across the term "C-set" with a fancy C, it just means "codeword."
Any sufficiently knowledgeable editor may delete any of these they deem irrelevant. The New Kid (talk) 09:20, 2 April 2023 (UTC)