#12418: adding Delsarte bound for codes
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Reporter: dimpase | Owner: wdj
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.5
Component: coding theory | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: #12533, #13650 | Stopgaps:
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Comment (by ppurka):
Replying to [comment:14 dimpase]:
> Replying to [comment:12 ppurka]:
> > I think the `Krawtchouk` polynomial could be computed explicitly by
not making repeated calls to `binomial`. This should speed it up.
>
> It's probably even faster to compute by using recurrence relations, but
I don't think it's important here: LP solving timing clearly dominates the
rest.
The point is that someone might try to use these polynomials more
generally in a separate context. They are not defined anywhere else in
Sage, so anyone who tries to use them will use this one.
> By the way, would it be interesting to include an option to compute
bounds on codes with a prescribed forbidden
> set of distances, rather than just [1..d] ? It's a trivial add-on.
> I did this in a prototype code for Johnson schemes,
[http://mathoverflow.net/questions/111603/intersecting-4-sets/111647#111647
here].
Wow! You have the !Johnson scheme too?! Sure, add them all in!! Do you use
the polynomials used by !Aaltonen?
> Any other interesting schemes to include? (Johnson scheme takes care of
constant weight binary codes, as you know.)
!LP for permutation codes would be interesting. There are not too many
good results known there. IIRC, it uses !Chebychev polynomials(?).
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12418#comment:16>
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