Gabidulin Codes

[5b3bd7e6-c3f3-4830-a555-991f5e6beec0]

A Linear Gabidulin Code Gab[n,k] over F{q^m} of length n <= m and dimension k <= n is the set of all words, formed by the operator evaluation of a q-degree restricted skew polynomial (with frobenius endomorphism and a finite field) f(x) \in S{F_{q^m}}[x].

i.e. Gab[n,k] = {(f(g_0), f(g1),..., f(g{n-1})) = f(g): deg(f) < k}

where g0,...,g{n-1} are fixed elements belonging to F{q^m} and are linearly independent over F{q}

This ticket proposes a new class for Gabidulin Codes along with encoders and decoders for it.

CC: @sagetrac-dlucas @johanrosenkilde @xcaruso @emes4 @Adurand8

Component: coding theory

Author: Arpit Merchant, Marketa Slukova

Branch: 64af632

Reviewer: Dima Pasechnik, Johan Rosenkilde

Issue created by migration from https://trac.sagemath.org/ticket/20970

[fchapoton]

comment:39

Nobody cared about the patchbot plugins. Please do in your next tickets.

[dimpase]

comment:40

Patchbots are often not kicking in quickly enough to notice anything interesting. But yes, I agree these things ought to be cleaned up on a followup ticket - I just opened #30348