Let K/k be a cyclic Galois extension of degree ℓ and θ a generator of Gal(K/k). For any v = (v 1 ,. .. , v m) ∈ K m such that v is linearly independent over k, and any 1 ≤ d < m the Gabidulin-like code C(v, θ, d) ≤ k ℓ×m is a maximum rank distance code of dimension ℓd over k. This construction unifies the ones available in the literature. We characterise… (More)
We develop a network coding technique based on flags of subspaces and a corresponding network channel model. To define error correcting codes we introduce a new distance on the flag variety, the Grassmann distance on flags and compare it to the commonly used gallery distance for full flags.