Codes in the sum-rank metric have attracted significant attention for their applications in
distributed storage systems, multishot network coding, streaming over erasure channels …

We provide an algebraic description for sum-rank metric codes, as quotient space of a skew
polynomial ring. This approach generalizes at the same time the skew group algebra setting …

We provide a geometric characterization of k-dimensional F q m-linear sum-rank metric
codes as tuples of F q-subspaces of F qm k. We then use this characterization to study one …

Guruswami and **ng introduced subspace designs in 2013 to give the first construction of
positive rate rank metric codes list-decodable beyond half the distance. In this paper we …

Sum-rank-metric codes have wide applications in universal error correction, multishot
network coding, space-time coding and the construction of partial-MDS codes for repair in …

We introduce the first geometric construction of codes in the sum-rank metric, which we
called linearized Algebraic Geometry codes, using quotients of the ring of Ore polynomials …

The sum-rank metric can be seen as a generalization of both, the rank and the Hamming
metric. It is well known that sum-rank metric codes outperform rank metric codes in terms of …

We investigate the asymptotic density of error-correcting codes with good distance
properties and prescribed linearity degree, including (sub) linear and nonlinear codes. We …

Linearized Reed-Solomon (LRS) codes are sum-rank metric codes that fulfill the Singleton
bound with equality. In the two extreme cases of the sum-rank metric, they coincide with …

Linearized Reed-Solomon (LRS) codes are a class of evaluation codes based on skew
polynomials. They achieve the Singleton bound in the sum-rank metric, and therefore are …