In this article we construct a new family of linear maximum rank distance (MRD) codes for all
parameters. This family contains the only known family for general parameters, the …

Rank-metric codes are codes consisting of matrices with entries in a finite field, with the
distance between two matrices being the rank of their difference. Codes with maximum size …

We compare the two duality theories of rank-metric codes proposed by Delsarte and
Gabidulin, proving that the former generalizes the latter. We also give an elementary proof of …

Let K/k be a cyclic Galois extension of degree ℓ ℓ and θ θ a generator of Gal (K/k). For any
v=(v_1, ..., v_m) ∈ K^ mv=(v 1,…, vm)∈ K m such that v is linearly independent over k, and …

In this paper, we survey the main known constructions of Ferrers diagram rank-metric codes,
and establish new results on a related conjecture by Etzion and Silberstein. We also give a …

We review the main results of the theory of error-correcting codes with the rank metric,
introducing combinatorial techniques for their analysis. We study their duality theory and …

Let O be a compact discrete valuation ring of characteristic 0. Given a module M of matrices
over O, we study the generating function encoding the average sizes of the kernels of the …

Subspace codes are the $ q $-analog of binary block codes in the Hamming metric. Here the
codewords are vector spaces over a finite field. They have eg applications in random linear …

We define the rank metric zeta function of a code as a generating function of its normalized q-
binomial moments. We show that, as in the Hamming case, the zeta function gives a …

Equidistant subspace codes are studied. A classification of the largest 1-intersecting codes
in PG (5, 2), whose codewords are planes, is provided. Also, new constructions of large …