#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 | 29b8892169f34a763c6e1be45a9d7cbba89dd811
Dependencies: #18928, #19897 | Stopgaps:
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Comment (by jsrn):
> But in the case `//`, the same snippet returns an `AssertionError`!
> I'm really stuck here. If anyone has an idea, I'll be glad to hear it.
The code has minimum distance 2, so it's OK that it can't decode 1 error.
Or?
The correct is `floor( (n+k)/2 )`. Note that in the current code, the
floor function is around `n+k`, and not around the division by two. You
can do `//` as Julien suggests, or move the floor function around the
division.
Gao's paper is very complicated to read, though the algorithm is so
simple. It's rather silly really -- it would have been much clearer to
formulate the stopping criterion as `deg s + k > deg r`. That's how you
would phrase it when using lattice basis reduction. It implies `deg r <
floor( (n+k)/2 )` under the assumption that `deg s < floor( (n-k)/2 )`.
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Ticket URL: <http://trac.sagemath.org/ticket/19653#comment:28>
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