#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 | 4aebb5a23a3c571f945bb7da558e03ff4b4c1ace
Dependencies: #18928, #19897 | Stopgaps:
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Comment (by dlucas):
Hello,
I changed what you asked, except the integer division in Gao decoder. I
re-read Gao's paper and it's indeed unclear.
So I tried the empirical method, and ran some tests.
In the case `/` this snippet:
{{{
sage: C = codes.GeneralizedReedSolomonCode(GF(59).list()[:40], 39)
sage: D = C.decoder("Gao")
sage: Chan = channels.StaticErrorRateChannel(C.ambient_space(), 1)
sage: for i in range(100):
....: c = C.random_element()
....: y = Chan(c)
....: assert c == D.decode_to_code(y)
}}}
indeed returns the "too-high degree" weird error...
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.
David
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Ticket URL: <http://trac.sagemath.org/ticket/19653#comment:26>
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