#18928: A new structure for Reed-Solomon codes in Sage
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Reporter: dlucas | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.8
Component: coding theory | Keywords:
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies: #18376, #18813
Stopgaps: |
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This ticket proposes a new implementation for Generalized Reed-Solomon
codes in Sage.
It contains:
- a new code class, `GeneralizedReedSolomonCode`, which wraps Reed-Solomon
code in the object-oriented structure introduced in #18099,
- a first new encoder, `GRSEvaluationVectorEncoder`, which can encode
words from a message space which is a vector space, and
- a second new encoder, `GRSEvaluationPolynomialEncoder`, which can encode
words from a message space which is a polynomial ring.
This new implementation properly sets GRS codes in the object-oriented
structure, which allows the user to use specific methods and algorithms to
encode (and later decode) words. It also introduces the notion of
generalized Reed-Solomon codes, which means that the user can now set a
list of column multipliers for the code.
It also allows to compute parity-check matrix and generator matrix from
the parameters of the code, through dedicated methods.
As GRS codes are now objects in Sage, it is also possible to ask a GRS
code for its specific parameters (like the list of its evaluation points,
or its column multipliers).
The two provided encoders follow the structure introduced in #18376.
More details about GRS codes can be found in the docstring of the provided
code.
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Ticket URL: <http://trac.sagemath.org/ticket/18928>
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