TY - JOUR
T1 - Orthogonal Frames in the Leech Lattice and a Type II Code over Z22
AU - Gulliver, T. Aaron
AU - Harada, Masaaki
N1 - Funding Information:
1This work was partially supported by the Sumitomo Foundation (No. 990645), Japan.
PY - 2001/7
Y1 - 2001/7
N2 - In this paper, we consider the problem of the existence of a basis of orthogonal vectors of norm 2k in the Leech lattice. Recently it has been shown that there is such a basis for every k (≥2) which is not of the form 11r. In this paper, this problem is completely settled by finding such a basis for k=11. This is established by constructing an extremal Type II Z22-code of length 24.
AB - In this paper, we consider the problem of the existence of a basis of orthogonal vectors of norm 2k in the Leech lattice. Recently it has been shown that there is such a basis for every k (≥2) which is not of the form 11r. In this paper, this problem is completely settled by finding such a basis for k=11. This is established by constructing an extremal Type II Z22-code of length 24.
UR - http://www.scopus.com/inward/record.url?scp=0009491946&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0009491946&partnerID=8YFLogxK
U2 - 10.1006/jcta.2000.3159
DO - 10.1006/jcta.2000.3159
M3 - Article
AN - SCOPUS:0009491946
VL - 95
SP - 185
EP - 188
JO - Journal of Combinatorial Theory - Series A
JF - Journal of Combinatorial Theory - Series A
SN - 0097-3165
IS - 1
ER -