#16597: Singer difference set and fix OA_9_135
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Reporter: vdelecroix | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.3
Component: combinatorial | Resolution:
designs | Merged in:
Keywords: | Reviewers:
Authors: Vincent Delecroix | Work issues:
Report Upstream: N/A | Commit:
Branch: | f725726fa68094215f1d4e19fac2378c0c29d3e8
u/vdelecroix/16597 | Stopgaps:
Dependencies: |
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Comment (by vdelecroix):
Hi,
> - In the doc of `are_projective_space_parameters` you give the equations
that `v,k,lmbda` must satisfy, but could you say it "with words" before
that ? Something like "such that the projective geometry of parameters
xx,xx,xx is a xx,xx,xx design ?"
will do: these are the parameters of a projective space design (assuming
that they only exists for prime powers ;-)
> - I had begun to write a commit linking this function with
`ProjectiveGeometryDesign` but I did not know enough to finish the review
`^^;`
Yeah it would be cool to check the t-design parameters of projective
geometry designs fit what `are_projective_space_parameters` check for.
Actually, it would make sense to move `are_projective_space_parameters` to
`block_design.py`. What do you think?
> - I do not understand the code yet, but don't you want to use the
'conway=True` trick in `singer_difference_set` ?
Nope. I need relative extensions `GF(q) -> GF(q^(d+1))`. The trick would
only "work" for prime fields. Moreover, testing if an element of an
extension belongs to the span over `GF(q)` of `(1,z,...,z^(d-1))` is a
mess (and trivial if you deal directly with polyonials).
I agree that I mimic an extension of `GF(q)` by dealing with polynomials
mod `c` (the relative Conway polynomial), but it seems the easiest way to
go.
Vincent
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Ticket URL: <http://trac.sagemath.org/ticket/16597#comment:16>
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