#19666: Guruswami-Sudan decoder for GRS 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: Johan Sebastian | Reviewers: dlucas
Rosenkilde Nielsen, David Lucas | Work issues:
Report Upstream: N/A | Commit:
Branch: | 0c7b80d275d22ad900eaaaec5c92352bbdf37b8b
u/jsrn/gs_list_decoding | Stopgaps:
Dependencies: #18928 |
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Comment (by jsrn):
This is not necessarily a bug but more a discussion: if there are no
nearby codewords this implementation is going to return an empty list. If
`s = ell = 1` then the Guruswami-Sudan algorithm is mathematically
equivalent to the Berlekamp-Welch, see #19653. If there are no nearby
codewords (i.e. with `d/2` radius), then *that* implementation will throw
a `DecodingError`. But this implementation will just return `[]`.
I'm not saying that's necessarily wrong. Having a list decoder, you'd like
to use `[]` as a valid response. It just means that the algorithm finished
completely as it should, and there were no nearby codewords. I just want
to be sure that we take this decision with open eyes, and that we possibly
document it somewhere.
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Ticket URL: <http://trac.sagemath.org/ticket/19666#comment:25>
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