#19422: A new structure for Punctured Codes
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Reporter: dlucas | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.10
Component: coding theory | Resolution:
Keywords: | Merged in:
Authors: David Lucas | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/dlucas/punctured_codes | ca859cbf3e6b86ccc218d6e51813ae45b9babb34
Dependencies: | Stopgaps:
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Old description:
> This ticket proposes a new implementation for punctured codes.
>
> It contains:
>
> - a new code class, `PuncturedCode`
>
> - a dedicated encoder to compute the generator matrix of a Punctured
> Code.
>
> This new structure presents the following advantages:
>
> - it keeps track of the code it comes from. If one punctures a code A,
> the punctured code he gets will remember it comes from A.
>
> - This allows to perform several operations, like encoding or picking a
> random element without constructing the generator matrix for the
> punctured code, thus saving time and memory.
>
> - Later on, it will also allow to decode words using a decoder over the
> original code of the punctured code.
New description:
This ticket proposes a new implementation for punctured codes.
It contains:
- a new code class, `PuncturedCode`
- a dedicated encoder to compute the generator matrix of a Punctured Code.
- a dedicate decoder which uses the original code to correct errors
This new structure presents the following advantages:
- it keeps track of the code it comes from. If one punctures a code A, the
punctured code one gets will remember it comes from A.
- This allows to perform several operations, like encoding or picking a
random element without constructing the generator matrix for the punctured
code, thus saving time and memory.
- because it keeps track of the original code, it's possible to get a
structured representation of the punctured code, e.g. if one punctures a
GRS code and asks for the structured representation of the punctured code
one got, a GRS code will be returned.
--
Comment (by dlucas):
A few updates on this ticket:
- it's now under the latest beta
- as we now have the structure for decoders in Sage, I added a dedicated
decoder for punctured codes
- as we now have GRS codes in Sage, which still are GRS codes after
puncturing, I introduced a mechanism which allows one to get the most
specific representation possible for a punctured code, based on the
original code.
This is still open for review.
--
Ticket URL: <http://trac.sagemath.org/ticket/19422#comment:10>
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