#20970: Gabidulin Codes
-------------------------------------+-------------------------------------
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 | 799d8713e4f49ff7301633fe6313271ad2082062
Dependencies: #13215 | Stopgaps:
-------------------------------------+-------------------------------------
Comment (by jsrn):
Replying to [comment:7 arpitdm]:
> Oh! I thought I only added the gabidulin.py file to my commit. Is there
a way I can remove the skew polynomial files from this ticket?
I guess you merged in the current tip of #13215 and that's what is showing
up as a long list of commits? That's perfectly ok (#13215 is a dependency
of this ticket).
> Also, @jsrn, you mention I computed g^q^t in the generator matrix of the
code. According to Equation 2.27 of the PhD thesis, there is no sigma in
the formation of the elements of the generator matrix.
Well, due to sigma always being the Frobenius, then `sigma^t(g)` is, by
definition, `g^(q^t)`. Wachter-Zeh just chose to write things using
explicit `q`-powering notation everywhere, instead of writing sigma. But
it is more mathematically elegant to write sigma, and it fits better with
the rest of the code. (say for instance that we choose to make a parameter
that you can construct Gabidulin codes with sigma be a power of Frobenius,
e.g. `sigma(g) = g^(q^2)`. These are sometimes, somewhat ridiculously,
called "Generalized Gabidulin codes").
--
Ticket URL: <https://trac.sagemath.org/ticket/20970#comment:10>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at https://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
