Binary additive MRD codes with minimum distance $$n-1$$n-1 must contain a semifield spread set

In this paper we prove a result on the structure of the elements of an additive maximum rank distance (MRD) code over the field of order two, namely that in some cases such codes must contain a semifield spread set. We use this result to classify additive MRD codes in $$M_n(\mathbb {F}_2)$$Mn(F2) with minimum distance $$n-1$$n-1 for $$n\le 6$$n≤6. Furthermore we present a computational classification of additive MRD codes in $$M_4(\mathbb {F}_3)$$M4(F3). The computational evidence indicates that MRD codes of minimum distance $$n-1$$n-1 are much more rare than MRD codes of minimum distance n, i.e. semifield spread sets. In all considered cases, each equivalence class has a known algebraic construction.

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