Higher Grassmann codes II

We compute the parameters of the linear codes that are associated with higher dimensional projective embeddings of Grassmannian when the degree exceeds the number of elements of the finite field. We investigate various dimension formulas for the projective Reed-Muller codes. We show that the duals of higher Grassmann codes are given by higher Grassmann codes or their simple extensions.(c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons .org /licenses /by -nc -nd /4 .0/).