On -Steiner systems from rank metric codes |
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Authors: | Francisco Arias Javier de la Cruz Joachim Rosenthal Wolfgang Willems |
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Institution: | 1. Universidad del Norte, Barranquilla, Colombia;2. University of Zurich, Switzerland;3. Otto-von-Guericke Universität, Magdeburg, Germany |
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Abstract: | In this paper we prove that rank metric codes with special properties imply the existence of -analogs of suitable designs. More precisely, we show that the minimum weight vectors of a dually almost MRD code which has no code words of rank weight form a -Steiner system . 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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Keywords: | Rank metric code Dually AMRD code |
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