TY - JOUR
T1 - Self-orthogonal 3-(56,12,65) designs and extremal doubly-even self-dual codes of length 56
AU - Harada, Masaaki
PY - 2006/1
Y1 - 2006/1
N2 - In this paper, we show that the code generated by the rows of a block-point incidence matrix of a self-orthogonal 3-(56,12,65) design is a doubly-even self-dual code of length 56. As a consequence, it is shown that an extremal doubly-even self-dual code of length 56 is generated by the codewords of minimum weight. We also demonstrate that there are more than one thousand inequivalent extremal doubly-even self-dual [56,28,12] codes. This result shows that there are more than one thousand non-isomorphic self-orthogonal 3-(56,12,65) designs.
AB - In this paper, we show that the code generated by the rows of a block-point incidence matrix of a self-orthogonal 3-(56,12,65) design is a doubly-even self-dual code of length 56. As a consequence, it is shown that an extremal doubly-even self-dual code of length 56 is generated by the codewords of minimum weight. We also demonstrate that there are more than one thousand inequivalent extremal doubly-even self-dual [56,28,12] codes. This result shows that there are more than one thousand non-isomorphic self-orthogonal 3-(56,12,65) designs.
KW - Extremal doubly-even self-dual code
KW - Self-orthogonal design
UR - http://www.scopus.com/inward/record.url?scp=29344458036&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=29344458036&partnerID=8YFLogxK
U2 - 10.1007/s10623-004-5657-6
DO - 10.1007/s10623-004-5657-6
M3 - Article
AN - SCOPUS:29344458036
SN - 0925-1022
VL - 38
SP - 5
EP - 16
JO - Designs, Codes, and Cryptography
JF - Designs, Codes, and Cryptography
IS - 1
ER -