#20970: Gabidulin Codes
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Reporter: arpitdm | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-7.3
Component: coding theory | Resolution:
Keywords: | Merged in:
Authors: Arpit Merchant | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/arpitdm/gabidulin_codes | ddaef4138cf29d70428a80539d249461226fbc9d
Dependencies: #13215 | Stopgaps:
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Changes (by arpitdm):
* commit: => ddaef4138cf29d70428a80539d249461226fbc9d
Comment:
A few points:
1. I've not added the tests and documentation for now since the code
design is still in flux.
2. The file compiles successfully and one can create the code and
codewords in vector form, i.e. F_{q^m^}^n^.
3. One problem right now is that, although the dual code and the parity
check matrix that are constructed are correct (verified by trying G*H^T^ =
0, as well as checking linear independence of h_0, h_1,..., h_{n-1}), I am
using a random element from the right kernel of the coefficient matrix
(Equation 2.28 of Antonia Wachter-Zeh's PhD thesis). And so dual of the
dual code does not give me the original code. `solve_right` returns the
trivial (all-zeros) solution.
4. Should there be a `def generator_matrix` method within the code class
itself?
----
New commits:
||[https://git.sagemath.org/sage.git/commit?id=ddaef4138cf29d70428a80539d249461226fbc9d
ddaef41]||{{{Initial construction of the Gabidulin Code class.
PolynomialEvaluationEncoder and GeneratorMatrixEncoder also included.}}}||
--
Ticket URL: <https://trac.sagemath.org/ticket/20970#comment:2>
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