Journal article · Preprint article
Affine Grassmann codes
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.
Language: | English |
---|---|
Publisher: | IEEE |
Year: | 2010 |
Pages: | 3166-3176 |
ISSN: | 15579654 and 00189448 |
Types: | Journal article and Preprint article |
DOI: | 10.1109/TIT.2010.2048470 |
ORCIDs: | Beelen, Peter |
14M15 15A24 94B05 94B27 Error correction codes Galois fields Linear code Mathematics Polynomials Reed-Muller codes affine Grassmann codes automorphism group cs.IT error correction codes linear codes linear error correcting codes math.AG math.IT minimum weight codewords number of minimum weight codewords