Affine Grassmann Codes

Details Affine Grassmann Codes Affine Grassmann Codes

2009-11-06

arxiv.org/abs/0911.1298v2

IEEE Trans. Inform. Theory 56 (2010), no. 7, 3166-3176

Computer Science

Information Theory

Slightly Revised Version; 18 pages

Scientific paper

10.1109/TIT.2010.2048470

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.

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