TY - JOUR
T1 - Self-Dual Codes and the Nonexistence of a Quasi-Symmetric 2-(37,9,8) Design with Intersection Numbers 1 and 3
AU - Harada, Masaaki
AU - Munemasa, Akihiro
AU - Tonchev, Vladimir D.
N1 - Funding Information:
The authors would like to thank the anonymous referees for carefully reading the manuscript. This work was supported by JSPS KAKENHI Grant Number 15H03633. Vladimir D. Tonchev acknowledges support by NSA Grant H98230-16-1-0011.
PY - 2017/10
Y1 - 2017/10
N2 - We prove that a certain binary linear code associated with the incidence matrix of a quasi-symmetric 2-(37, 9, 8) design with intersection numbers 1 and 3 must be contained in an extremal doubly even self-dual code of length 40. Using the classification of extremal doubly even self-dual codes of length 40, we show that a quasi-symmetric 2-(37, 9, 8) design with intersection numbers 1 and 3 does not exist.
AB - We prove that a certain binary linear code associated with the incidence matrix of a quasi-symmetric 2-(37, 9, 8) design with intersection numbers 1 and 3 must be contained in an extremal doubly even self-dual code of length 40. Using the classification of extremal doubly even self-dual codes of length 40, we show that a quasi-symmetric 2-(37, 9, 8) design with intersection numbers 1 and 3 does not exist.
KW - doubly even self-dual code
KW - quasi-symmetric 2-design
KW - self-orthogonal code
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U2 - 10.1002/jcd.21556
DO - 10.1002/jcd.21556
M3 - Article
AN - SCOPUS:85017166039
VL - 25
SP - 469
EP - 476
JO - Journal of Combinatorial Designs
JF - Journal of Combinatorial Designs
SN - 1063-8539
IS - 10
ER -