Affine Grassmann Codes
arXiv:0911.1298 · doi:10.1109/TIT.2010.2048470
Abstract
We consider a new class of linear codes, called affine Grassmann codes. These can be viewed as a variant of generalized Reed-Muller codes and are closely related to Grassmann codes. We determine the length, dimension, and the minimum distance of any affine Grassmann code. Moreover, we show that affine Grassmann codes have a large automorphism group and determine the number of minimum weight codewords.
Slightly Revised Version; 18 pages