Title :
Affine Grassmann Codes
Author :
Beelen, Peter ; Ghorpade, Sudhir R. ; HØholdt, Tom
Author_Institution :
Dept. of Math., Tech. Univ. of Denmark, Lyngby, Denmark
fDate :
7/1/2010 12:00:00 AM
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.
Keywords :
Reed-Muller codes; error correction codes; linear codes; Reed-Muller codes; affine Grassmann codes; automorphism group; linear error correcting codes; minimum weight codewords; Error correction codes; Galois fields; Linear code; Mathematics; Polynomials; Automorphism group; Grassmann codes; number of minimum weight codewords;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2010.2048470
