Duals of Affine Grassmann Codes and their Relatives

Abstract

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.

20 pages

References in corpus (2)

• Decomposable Subspaces, Linear Sections of Grassmann Varieties, and Higher Weights of Grassmann Codes
• Affine Grassmann Codes

Cited by in corpus (5)

• Automorphism groups of Grassmann codes
• Remarks on Tsfasman-Boguslavsky Conjecture and Higher Weights of Projective Reed-Muller Codes
• Minimum Distance and the Minimum Weight Codewords of Schubert Codes
• Enumerative Coding for Line Polar Grassmannians with applications to codes
• Affine Hermitian Grassmann Codes