Minimal Codewords in Linear Codes

Borissov, Yuri, and Manev, Nickolai. "Minimal Codewords in Linear Codes." Serdica Mathematical Journal 30.2-3 (2004): 303-324. <http://eudml.org/doc/219584>.

@article{Borissov2004,
abstract = {2000 Mathematics Subject Classification: 94B05, 94B15.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.},
author = {Borissov, Yuri, Manev, Nickolai},
journal = {Serdica Mathematical Journal},
keywords = {Codewords; Cyclic Codes; Binary Reed-Muller Code; Linear codes; Minimal codewords},
language = {eng},
number = {2-3},
pages = {303-324},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Minimal Codewords in Linear Codes},
url = {http://eudml.org/doc/219584},
volume = {30},
year = {2004},
}

TY - JOUR
AU - Borissov, Yuri
AU - Manev, Nickolai
TI - Minimal Codewords in Linear Codes
JO - Serdica Mathematical Journal
PY - 2004
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 30
IS - 2-3
SP - 303
EP - 324
AB - 2000 Mathematics Subject Classification: 94B05, 94B15.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.
LA - eng
KW - Codewords; Cyclic Codes; Binary Reed-Muller Code; Linear codes; Minimal codewords
UR - http://eudml.org/doc/219584
ER -