Affine Grassmann codes

Authors:
Peter Beelen;Sudhir R. Ghorpade;Tom Høholdt
Affiliations:
Department of Mathematics, Technical University of Denmark, Lyngby, Denmark;Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai, India;Department of Mathematics, Technical University of Denmark, Lyngby, Denmark
Venue:
IEEE Transactions on Information Theory
Year:
2010

Citing 4
Cited 0

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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.