Geodesic
Minimal Codewords in Linear Codes
Serdica Mathematical Journal, Tome 30 (2004) no. 2-3, pp. 303-324

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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.
Keywords: Codewords, Cyclic Codes, Binary Reed-Muller Code 
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     title = {Minimal {Codewords} in {Linear} {Codes}},
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Borissov, Yuri; Manev, Nickolai. Minimal Codewords in Linear Codes. Serdica Mathematical Journal, Tome 30 (2004) no. 2-3, pp. 303-324. http://geodesic.mathdoc.fr/item/SMJ2_2004_30_2-3_a10/