Optimum Distance Flag Codes from Spreads in Network Coding

05/19/2020

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by   Clementa Alonso-González, et al.

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We study multishot codes in network coding given by families of flags on a vector space F_q^n, being q a prime power and F_q the finite field of q elements. In particular, we characterize the type vector of flag codes that attain the maximum distance ( optimum distance flag codes) having a spread as the subspace code sent at some shot and we also provide a construction of these codes. A maximum distance constant dimension code with the best possible size, whenever the dimension divides n, must be a spread. In this paper we show that optimum distance flag codes attaining the best possible size, given an admissible type vector, must have a spread as the subspace code used at the corresponding shot.