TY - JOUR
T1 - On the classification of self-dual [20,10,9] codes over GF(7)
T2 - In memory of Yutaka Hiramine
AU - Harada, Masaaki
AU - Munemasa, Akihiro
N1 - Funding Information:
The authors would like to thank Sho Suda for useful discussions. The authors would also like to thank the anonymous referee for helpful comments. This work is supported by JSPS KAKENHI Grant Number 26610032 .
Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2016/11/1
Y1 - 2016/11/1
N2 - It is shown that the extended quadratic residue code of length 20 over GF(7) is a unique self-dual [20,10,9] code C such that the lattice obtained from C by Construction A is isomorphic to the 20-dimensional unimodular lattice D20+, up to equivalence. This is done by converting the classification of such self-dual codes to that of skew-Hadamard matrices of order 20.
AB - It is shown that the extended quadratic residue code of length 20 over GF(7) is a unique self-dual [20,10,9] code C such that the lattice obtained from C by Construction A is isomorphic to the 20-dimensional unimodular lattice D20+, up to equivalence. This is done by converting the classification of such self-dual codes to that of skew-Hadamard matrices of order 20.
KW - Self-dual code
KW - Skew-Hadamard matrix
KW - Unimodular lattice
UR - http://www.scopus.com/inward/record.url?scp=84978803743&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84978803743&partnerID=8YFLogxK
U2 - 10.1016/j.ffa.2016.07.004
DO - 10.1016/j.ffa.2016.07.004
M3 - Article
AN - SCOPUS:84978803743
SN - 1071-5797
VL - 42
SP - 57
EP - 66
JO - Finite Fields and Their Applications
JF - Finite Fields and Their Applications
ER -