On the non-minimal codewords in binary Reed--Muller codes

Authors:
Yuri Borissov;Nickolai Manev;Svetla Nikova
Affiliations:
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 G.Bonchev, 1113 Sofia, Bulgaria;Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 G.Bonchev, 1113 Sofia, Bulgaria;Dept. Electr. Eng. ESAT/COSIC, Katholieke Universiteit Leuven, Kardinal Mercierlaan 94, 3001 Heverlee, Belgium
Venue:
Discrete Applied Mathematics - Special issue: International workshop on coding and cryptography (WCC 2001)
Year:
2003

Citing 2
Cited 2

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Abstract

First, we compute the number of non-minimal codewords of weight 2dmin in the binary Reed-Muller code RM(r,m). Second, we prove that all codewords of weight greater than 2m - 2m-r+1 in binary RM(r,m), are non-minimal.