On q-analog Steiner systems of 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 [2d,d,d] dually almost MRD code C≤ Fqmn which has no code words of rank weight d+1 form a q-analog Steiner system Sq(d-1,d,2d). In particular, d+1 must be a prime.
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