Flag codes from planar spreads in network coding.

In this paper we study a class of multishot network codes given by families of nested subspaces (flags) of a vector space F q n , being q a prime power and F q the finite field of q elements. In particular, we focus on flag codes having maximum distance (optimum distance flag codes). We explore the existence of these codes from spreads, based on the good properties of the latter ones. For n = 2 k , we show that optimum distance full flag codes with the largest size are exactly those that can be constructed from a planar spread. We give a precise construction of them as well as a decoding algorithm. [ABSTRACT FROM AUTHOR]