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Affine Grassmann Codes

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3 Author(s)
Peter Beelen ; Department of Mathematics, Technical University of Denmark, Lyngby, Denmark ; Sudhir R. Ghorpade ; Tom Hoholdt

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.

Published in:

IEEE Transactions on Information Theory  (Volume:56 ,  Issue: 7 )