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Duals of Affine Grassmann Codes and Their Relatives

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Title Duals of Affine Grassmann Codes and Their Relatives
 
Creator BEELEN, P
GHORPADE, SR
HOHOLDT, T
 
Subject Automorphism group
dual code
Grassmann Codes
minimum weight codewords
REED-MULLER CODES
 
Description Affine Grassmann codes are a variant of generalized Reed-Muller codes and are closely related to Grassmann codes. These codes were introduced in a recent work by Beelen et al. Here, we consider, more generally, affine Grassmann codes of a given level. We explicitly determine the dual of an affine Grassmann code of any level and compute its minimum distance. Further, we ameliorate the results by Beelen et al. concerning the automorphism group of affine Grassmann codes. Finally, we prove that affine Grassmann codes and their duals have the property that they are linear codes generated by their minimum-weight codewords. This provides a clean analogue of a corresponding result for generalized Reed-Muller codes.
 
Publisher IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
 
Date 2014-10-17T04:59:19Z
2014-10-17T04:59:19Z
2012
 
Type Article
 
Identifier IEEE TRANSACTIONS ON INFORMATION THEORY, 58(6)3843-3855
http://dx.doi.org/10.1109/TIT.2012.2187171
http://dspace.library.iitb.ac.in/jspui/handle/100/16010
 
Language en