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We discuss the problem of determining the complete weight hierarchy of linearerror correcting codes associated to Grassmann varieties and, more generally,to Schubert varieties in Grassmannians. The problem is partially solved in thecase of Grassmann codes, and one of the solutions uses the combinatorial notionof a closed family. We propose a generalization of this to what is called asubclose family. A number of properties of subclose families are proved, andits connection with the notion of threshold graphs and graphs with maximum sumof squares of vertex degrees is outlined.

Subclose Families, Threshold Graphs, and the Weight Hierarchy of Grassmann and Schubert Codes