TY - JOUR
T1 - On the residue codes of extremal Type II ℤ 4-codes of lengths 32 and 40
AU - Harada, Masaaki
PY - 2011/10/28
Y1 - 2011/10/28
N2 - In this paper, we determine the dimensions of the residue codes of extremal Type II Z4-codes of lengths 32 and 40. We demonstrate that every binary doubly even self-dual code of length 32 can be realized as the residue code of some extremal Type II Z4-code. It is also shown that there is a unique extremal Type II Z4-code of length 32 whose residue code has the smallest dimension 6 up to equivalence. As a consequence, many new extremal Type II Z4-codes of lengths 32 and 40 are constructed.
AB - In this paper, we determine the dimensions of the residue codes of extremal Type II Z4-codes of lengths 32 and 40. We demonstrate that every binary doubly even self-dual code of length 32 can be realized as the residue code of some extremal Type II Z4-code. It is also shown that there is a unique extremal Type II Z4-code of length 32 whose residue code has the smallest dimension 6 up to equivalence. As a consequence, many new extremal Type II Z4-codes of lengths 32 and 40 are constructed.
KW - Binary doubly even code
KW - Extremal Type II -code
KW - Residue code
UR - http://www.scopus.com/inward/record.url?scp=84860395742&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84860395742&partnerID=8YFLogxK
U2 - 10.1016/j.disc.2011.06.022
DO - 10.1016/j.disc.2011.06.022
M3 - Article
AN - SCOPUS:84860395742
SN - 0012-365X
VL - 311
SP - 2148
EP - 2157
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 20
ER -