Fundamental Results on a Class of Affine Polar Grassmann Codes and Their Duals
Fernando Piñero, Doel Rivera-Laboy · IEEE Transactions on Information Theory · 2023
In this manuscript, we study affine polar Grassmann codes. These are linear codes associated to an affine part of the projective embedding of a polar Grassmannian. In particular, the length, dimension, and minimum distance of the affine polar Grassmann codes derived from the symplectic Grassmannian and the Hermitian Grassmannian of totally isotropic spaces are determined. It is also shown that affine Hermitian Grassmann codes have a better minimum distance than affine Grassmann codes while having the same length, dimension, and alphabet size. We also study their dual codes and their related incidence structure.