Short rank-metric codes and scattered subspaces
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By exploiting the connection between scattered 𝔽_q-subspaces of 𝔽_q^m^3 and minimal non degenerate 3-dimensional rank metric codes of 𝔽_q^m^n, n ≥ m+2, described in <cit.>, we will exhibit a new class of codes with parameters [m+2,3,m-2]_q^m/q for infinite values of q and m ≥ 5 odd. Moreover, by studying the geometric structures of these scattered subspaces, we determine the rank weight distribution of the associated codes.
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