The Schubert-union conjecture for higher weights of Grassmann codes

Let $G(l,m)$ be a Grassmann variety and let its associated Grassmann code have higher weights. A Schubert union is a union of Schubert varieties in the Grassmann variety. Schubert-union conjecture. The answer to Question (Q5) of Section is always affirmative; equivalently, the higher weights of the Grassmann codes are always computed by Schubert unions. The preceding theorem establishes the corresponding maximal-dimension result for linear sections, and the conjecture extends this phenomenon to all higher weights of Grassmann codes. Its status is not resolved in the supplied text.