Higher Grassmann codes III: their decoding and quantum variants

We show that it is possible to break up Higher Grassmann codes we constructed in earlier work to a sequence of affine Reed-Muller codes so that various operations such as decoding can be reduced to performing these operations for the component affine Reed-Muller codes. Then we consider quantum codes produced from a pair of Higher Grassmann codes and discuss also their encoding and decoding aspects in some detail.