#19418: skew-Hadamard matrices and related srg's
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Reporter: | Owner:
dimpase | Status: needs_work
Type: | Milestone: sage-6.10
enhancement | Resolution:
Priority: major | Merged in:
Component: | Reviewers: Nathann Cohen
combinatorics | Work issues:
Keywords: | Commit:
Authors: | c5a7eee39d4c6dce006d1f6f8fd7a23383d540b7
Report Upstream: N/A | Stopgaps:
Branch: |
public/19418 |
Dependencies: |
#19309 |
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Comment (by dimpase):
Replying to [comment:17 ncohen]:
> > (back to Oxford with huge jetlag)
>
> Wow. Common timezone again. Cool `;-)`
an hour difference, still :-)
>
> > `normalize_hadamard` does not do what I need; I need a different type
of normalization, in fact, where the matrix has the 1st row consisting of
1s, and still H+H.T==2*I,
> > i.e. the 1st column of H is all -1 (with exception of the top left
entry)
> >
> > Should I perhaps introduce `skew_normalize_hadamard`,
> > that can only be applied to skew Hadamard matrices?
> > (I'd have uses for it in graph constructions, too)
>
> Sounds right. Then you can have a proper documentation and stuff. If you
plan to use it elsewhere that's even better.
oops, this won't fly. The problem is that once a skew-Hadamard matrix was
de-skewed (e.g. by the usual normalization procedure, producing the 1st
row and column of 1s),
there is no general way known to make it skew again.
(and in fact not every Hadamard matrix can be made skew, AFAIK).
That is, I have to disable normalization right at the point it is done in
`hadamard_matrix_paleyI`. (writing an ad hoc code to undo this specific
normalization seems silly).
--
Ticket URL: <http://trac.sagemath.org/ticket/19418#comment:18>
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