Duals of Affine Grassmann Codes and their Relatives

Details Duals of Affine Grassmann Codes and their Relatives Duals of Affine Grassmann Codes and their Relatives

2011-07-18

arxiv.org/abs/1107.3438v1

Computer Science

Information Theory

20 pages

Scientific paper

Affine Grassmann codes are a variant of generalized Reed-Muller codes and are closely related to Grassmann codes. These codes were introduced in a recent work [2]. Here we consider, more generally, affine Grassmann codes of a given level. We explicitly determine the dual of an affine Grassmann code of any level and compute its minimum distance. Further, we ameliorate the results of [2] concerning the automorphism group of affine Grassmann codes. Finally, we prove that affine Grassmann codes and their duals have the property that they are linear codes generated by their minimum-weight codewords. This provides a clean analogue of a corresponding result for generalized Reed-Muller codes.

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