On q-Steiner systems from rank metric codes

Abstract In this paper we prove that rank metric codes with special properties imply the existence of q -analogs of suitable designs. More precisely, we show that the minimum weight vectors of a [ 2 d , d , d ] dually almost MRD code C ≤ F q m 2 d ( 2 d ≤ m ) which has no code words of rank weight d + 1 form a q -Steiner system S ( d − 1 , d , 2 d ) q . This is the q-analog of a result in classical coding theory and it may be seen as a first step to prove a q-analog of the famous Assmus–Mattson Theorem.

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