#19317: A (1288,792,476,504)-strongly regular graph
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Reporter: | Owner:
ncohen | Status: needs_review
Type: | Milestone: sage-6.9
enhancement | Resolution:
Priority: major | Merged in:
Component: graph | Reviewers:
theory | Work issues:
Keywords: | Commit:
Authors: | f6272d39e0de839ef4e28e28d3d8fd207fe6cbae
Nathann Cohen | Stopgaps:
Report Upstream: N/A |
Branch: |
u/ncohen/19317 |
Dependencies: |
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Comment (by dimpase):
Replying to [comment:4 ncohen]:
> > Do you really need the whole Golay code for this?
>
> You can add a commit if you prefer. I admit that I prefer it the way it
is written, as you can explain the construction a bit better than just
"some orbit will work". I don't mind either way.
"some orbit will work", as it is a rank 3 permutation representation of
`M_{24}`.
You can refer to Conway et al. Atlas of Finite Group. It was certainly
well-known long before the reference you provide.
It's also mind-boggling the way it is given, that it works. In fact, it's
a property of the extended Golay code (i.e.
`sage.coding.code_constructions.ExtendedBinaryGolayCode()`), that it only
has words of length 0,8,12,16, and 24), so you can relate the graph
vertices to certain 1288 partitions of the 24-set into 12+12, with
`M_{24}` acting in the natural way (`onSetsSets` ?).
You work with the shorter (length 23) code, on which `M_{24}` acts as a
linear group, so this is less transparent.
--
Ticket URL: <http://trac.sagemath.org/ticket/19317#comment:5>
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