#19623: Syndrome decoder is not a syndrome decoder
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Reporter: dlucas | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-7.0
Component: coding theory | Resolution:
Keywords: | Merged in:
Authors: David Lucas | Reviewers: Julien Lavauzelle
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/dlucas/generic_decoders | 54c02c3af22e896dd03759408b989f493415f26a
Dependencies: | Stopgaps:
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Comment (by jsrn):
Hi David,
I agree, David, that the "informing the code"-feature is advanced and
shouldn't be done in this ticket. Sorry for not making that clear.
So, firstly, I want to say that my comments actually make sense even as a
completely internal mechanism of `SyndromeDecoder`. That is, harvesting
the true minimum distance and covering radius while the lookup-table is
being build enables the decoder to give useful feedback to the user, such
as its decoding radius and a more precise decoder type.
Secondly, I hope you realise that this is "just" yet another example of
the usefulness of a general mechanism for specifying upper- and lower-
bounds on the minimum distance of a code, and it shows that, indeed as
could have been expected, that minimum distance is *not* special in this
regard: there are other parameters for which me might want such a
mechanism (in this case, covering radius).
To be more precise, say we design a general system for informing a
`LinearCode` that new knowledge has been obtained on a property it has. It
could be something like (and now I'm totally making this up on the spot):
{{{
`LinearCode._update_property_bound(property_name, update_type, value)
}}}
With such a mechanism, `SyndromeDecoder` would call
{{{
`self._code._update_property_bound("minimum_distance", "upper", t)
`self._code._update_property_bound("minimum_distance", "lower", t)
}}}
or simply
{{{
`self._code._update_property_bound("minimum_distance", "exact", t)
}}}
Then the function `minimum_distance` should be changed accordingly. And
various functions for computing or bounding the minimum distance should
also be changed accordingly.
As we have discussed before, we should be very careful not completely
over-engineering this. I think it might be useful to start compiling a
list of examples where such bound computation is possible and could be
useful.
--
Ticket URL: <http://trac.sagemath.org/ticket/19623#comment:20>
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