#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: | 10c9beb0a672b3b5c628d7b206b6dbc49aae5848
u/vdelecroix/16597 | Stopgaps:
Dependencies: #16553,#16617 |
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Comment (by vdelecroix):
Replying to [comment:27 ncohen]:
> Basically, I don't get why doint this does the job
>
> {{{
> + # now compute the set of i such that z^i belongs to the subspace
spanned by
> + # (1,z,z^2,...,z^(d-1)) over GF(q) (up to the action of scalar
> + # multiplication)
> }}}
>
> And it isn't exactly the way it is explained in Stinson's book either I
believe..
It follows Stinson but the loop is stopped sooner.
The field `Kbig` with q^e+1^ elements is a vector space over `Ksmall` the
one with q elements. We chose a generator z of the multiplicative group of
`Kbig` (that way we have a cyclic action on lines). We also choose a
concrete subspace of dimension `d` in `Kbig` to be the span (over
`Ksmall`) of 1,z,...z^d-1^. Let call it `V` this subspace.
The difference set is by definition the set of integers `i` such that
`z^i` belong to `V` (recall that any element of `Kbig` different from `0`
can be written as `z^i` with `i < q^e`).
This is what Stinson does and this is what I am doing.
Vincent
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Ticket URL: <http://trac.sagemath.org/ticket/16597#comment:28>
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