#19778: McFarland 1973 construction for difference sets
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Reporter: vdelecroix | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.0
Component: combinatorial | Resolution:
designs | Merged in:
Keywords: | Reviewers:
Authors: Vincent Delecroix | Work issues:
Report Upstream: N/A | Commit:
Branch: | b3dd88ae6ff747f6c67ca20948b58269dcac73cd
u/vdelecroix/19778 | Stopgaps:
Dependencies: |
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Comment (by ncohen):
Hello again,
I have been staring for a while at the parameters v,k,l, looking for a way
to avoid the database. Now number theory really isn't my thing, but I
wonder about that: shouldn't the gcd of 'v,l,m' be *very* close to `q^s`?
Actually, in the factorization of `gcd(v,l,m)` into `pi,si`, aren't we
sure that `q^s` is equal to the largest value of `pi^si`.
Actually (please tell me if I am wrong) by developping k as a series I get
that `k=lambda+q^(2s)`, thus `gcd(lambda,k)` is a power of `q` greater
than `q^s` (because both k and l can be divided by `q^s`).
I'm getting very convinced that `q^s` is actually equal to
`gcd(lambda,k)`.
Well, what do you think? `:-/`
Nathann
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Ticket URL: <http://trac.sagemath.org/ticket/19778#comment:12>
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