#19422: A new structure for Punctured Codes
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Reporter: dlucas | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-7.2
Component: coding theory | Resolution:
Keywords: | Merged in:
Authors: David Lucas | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/dlucas/punctured_codes | 69da167f0a9d4a0fc68e0846416577a5ddb44eba
Dependencies: #19653 | Stopgaps:
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Changes (by jlavauzelle):
* status: needs_review => needs_work
Comment:
*** src/sage/coding/punctured_code.py ***
--- function `puncture` ---
- same strange way to compute the non-punctured positions than in grs.py.
For example, it doesn't work with:
{{{
C = codes.RandomLinearCode(11, 5, GF(7))
Cp = codes.PuncturedCode(C, [4,3])
v = vector(GF(7), (2,3,0,2,1,5,1,5,6,5,3))
sage.coding.punctured_code.puncture(v, [4,3], Cp)
}}}
--- class `PuncturedCode` ---
- constructor:
`positions = list(set(positions))` is a short (maybe dirty) way to do:
{{{
unique_positions = set()
for i in positions:
unique_positions.add(i)
positions = []
for i in unique_positions:
positions.append(i)
}}}
and it looks to sort the elements as well =) Also remark that you don't
have this "multiplicity" issue when using Python sets (instead of lists)
for storing puncturing points.
- in encode() method, you missed parentheses after
`self.punctured_positions` in `return puncture(c,
self.punctured_positions, self)`
- in structured_representation(self) method: in the doc, you wrote "A
punctured GRS code is still a punctured code" but I think you meant "still
a GRS code". Moreover, I don't understand what you mean by "Which is not
the case for generic linear codes": punctured linear codes are still
linear codes.
- still in structured_representation(self) method, I tried this:
{{{
sage: C = codes.GeneralizedReedSolomonCode(GF(7).list(), 4)
sage: P = codes.PuncturedCode(C, [1,3])
sage: Q = codes.PuncturedCode(P, [1,3])
sage: P.length()
5
sage: Q.length()
3
sage: P.structured_representation()
[5, 4, 2] Generalized Reed-Solomon Code over Finite Field of size 7
sage: Q.structured_representation()
[5, 3, 3] Generalized Reed-Solomon Code over Finite Field of size 7
}}}
So, double puncturing works well (`Q` seems to be the right code), but
`structured_representation()` doesn't build the right Reed-Solomon code.
--- class `PuncturedCodePuncturedMatrixEncoder` ---
- in `GeneratorMatrix`: same comment as in linear_code.py, I think
echelon_form()do the job and you just need to keep the `k` first rows.
--- class `PuncturedCodeOriginalCodeDecoder` ---
- sage is stuck (infinite loop ?) when I run this:
{{{
sage: R = codes.RandomLinearCode(11, 5, GF(7))
sage: P = codes.PuncturedCode(R, [1,3])
sage: P.decoder()
}}}
- l.444: you wrote ``'random_values'`` instead of ``'random-values'``
- in the constructor: you have a test variable `error_erasure` to which
you assign `0` and `1`. Maybe `True` and `False` are more explicit.
- in `decode_to_code`: l.600, I think you forgot to increment `shift`
(otherwise I misunderstood the use of `shift`)
- maybe add an `elif self._strategy == 'try-all'` at line 643.
- l.670: `ValueError("The number of erasures exceed decoding capability")`
--> exceeds
- l.672: decoding capability must be:
{{{
return (diff - punctured -1) // 2
}}}
- l.665; you could have negative radius with:
{{{
if self._strategy != 'try-all' and "error-erasure" not in
D.decoder_type():
return D.decoding_radius() - punctured
}}}
- I don't understand the last `return D.decoding_radius()`, line 675. To
which case does it apply ?
--
Ticket URL: <http://trac.sagemath.org/ticket/19422#comment:21>
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