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Title: Minimal Codewords in Linear Codes
Authors: Borissov, Yuri
Manev, Nickolai
Keywords: Codewords
Cyclic Codes
Binary Reed-Muller Code
Issue Date: 2004
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 30, No 2-3, (2004), 303p-324p
Abstract: Cyclic binary codes C of block length n = 2^m − 1 and generator polynomial g(x) = m1(x)m2^s+1(x), (s, m) = 1, are considered. The cardinalities of the sets of minimal codewords of weights 10 and 11 in codes C and of weight 12 in their extended codes ^C are determined. The weight distributions of minimal codewords in the binary Reed-Muller codes RM (3, 6) and RM (3, 7) are determined. The applied method enables codes with larger parameters to be attacked.
Description: 2000 Mathematics Subject Classification: 94B05, 94B15.
ISSN: 1310-6600
Appears in Collections:Volume 30 Number 2-3

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