#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 dimpase):
Replying to [comment:16 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.
Actually, I have most discrete orthogonal polynomials arising in the
classical P- and Q- polynomial schemes
[https://bitbucket.org/dimpase/qcode/src/9e3b79dc71992aa2a8ea170dbd13f9f373772411/aw.sage?at=default
implemented], although it's neither polished nor optimized.
[
>
> > 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?
I
[https://bitbucket.org/dimpase/qcode/src/9e3b79dc71992aa2a8ea170dbd13f9f373772411/aw.sage?at=default
use] the descriptions in the book "Algebraic Combinatorics I" by E.Bannai
and T.Ito.
Something known as [http://mathworld.wolfram.com/EberleinPolynomial.html
Eberlein polynomials].
>
> > 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(?).
yes, this should be perfectly doable.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12418#comment:18>
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