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LetK/k be a cyclic Galois extension of degree l and θ a generator of Gal(K/k). For any v = (v1, . . . , vm) ∈ K m such that v is linearly independent over k, and any 1 ≤ d < m the Gabidulin-like code C(v, θ, d) ≤ kl×m is a maximum rank distance code of dimension ld over k. This construction unifies the ones available in the literature. We characterise the… (More)
Abstract. 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.