#19653: New decoders for Generalized Reed-Solomon codes
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Reporter: dlucas | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.1
Component: coding theory | Resolution:
Keywords: | Merged in:
Authors: David Lucas | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/dlucas/grs_decoders | 7cbcca2969f5a72776eaff64951318a6c3c89a84
Dependencies: #18928, #19897 | Stopgaps:
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Comment (by dlucas):
Yum, border cases! I'll investigate this.
Regarding your
> *'''Another remark'''*
your example actually works. See as follows:
{{{
sage: C = codes.GeneralizedReedSolomonCode(GF(59).list()[:40], 12)
sage: c = C.random_element()
sage: Chan = channels.StaticErrorRateChannel(C.ambient_space(),
C.decoder().decoding_radius())
sage: y = Chan(c)
sage: c == C.encode(C.decode_to_message(y))
True
}}}
What might be bothering you is:
{{{
sage: C.decoder().connected_encoder() == C.encoder()
False
}}}
But actually, `AbstractLinearCode.decode_to_message` has been written such
that it *always* returns the element of the message space as a vector,
because it seems the more natural way of seeing messages. This generic
`decode_to_message` is more designed for beginners/people who don't want
to bother with all the underlying structure, thus we defaulted the the
most intuitive representation.
And that's one of the reasons for which we ask `default_encoder` to be
always set to an encoder whose `message_space` is a vector space.
David
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Ticket URL: <http://trac.sagemath.org/ticket/19653#comment:22>
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