Rank-metric codes over arbitrary Galois extensions and rank analogues of Reed-Muller codes

Daniel Augot, Alain Couvreur, Julien Lavauzelle +1

This paper extends the study of rank-metric codes in extension fields $\mathbb{L}$ equipped with an arbitrary Galois group $G=\mathrm{Gal}(\mathbb{L}/\mathbb{K})$. We propose a f…