#19623: Syndrome decoder is not a syndrome decoder
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Reporter: dlucas | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.0
Component: coding theory | Resolution:
Keywords: | Merged in:
Authors: David Lucas | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/dlucas/generic_decoders | fc79446d6948143d32a9065410453379c79ef2b2
Dependencies: | Stopgaps:
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Comment (by dlucas):
> Since the covering radius of a linear code is always at most n-k, does
it make any sense to let the table search beyond that?
Not really. I'll change this.
> Did you prove that if there are no coset leaders of weight t, then there
are no coset leaders of t+1? (i.e. that your early termination is sound)
It comes from theorem 1.12.6, prop. 5 in Huffman and Pless
Theorem 1.12.6 Let C be an [n, k] code over F q . Let C*
a code obtained from C by puncturing on some coordinate. The following
hold:
(v) Assume that x is a coset leader of C. If x' ∈ `(F_q)^n` all of whose
nonzero components agree
with the same components of x, then x' is also a coset leader of C. In
particular, if
there is a coset of weight s, there is also a coset of any weight less
than s.
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Ticket URL: <http://trac.sagemath.org/ticket/19623#comment:8>
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