Galois geometries and coding theory are two research areas which have been interacting
with each other for many decades. From the early examples linking linear MDS codes with …

Repair locality has been an important metric in a distributed storage system (DSS). Erasure
codes with small locality are more popular in a DSS, which means fewer available nodes …

In this paper we study a class of multishot network codes given by families of nested
subspaces (flags) of a vector space F qn, being qa prime power and F q the finite field of q …

Constant dimension codes are subsets of the finite Grassmann variety. The subspace
distance is a natural metric on the Grassmannian. It is desirable to have constructions of …

In this paper, we study flag codes on the vector space F _q^ n F qn, being qa prime power
and F _q F q the finite field of q elements. More precisely, we focus on flag codes that attain …

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 …

In this paper we study equidistant subspace codes, ie subspace codes with the property that
each two distinct codewords have the same distance. We provide an almost complete …

Distributed storage systems based on intersecting constant dimension (equidistant) codes
are presented. These intersecting codes are constructed using the Plücker embedding …

Rank distance codes are known to be applicable in various applications such as distributed
data storage, cryptography, space time coding, and mainly in network coding. Rank distance …

An-locally repairable code (LRC) is called a Singleton-optimal LRC if it achieves the
Singleton-type bound. Analogous to the classical MDS conjecture, the maximal length …