OFFSET
0,2
COMMENTS
L1 norm of (a,b,c,...) = |a|+|b|+|c|+...
A lower bound if n = 2^m >= 4: a(n) >= 2n^2 + Sum_{r=2..[log_2 n]} A(2^r,2^(r-1))*A(n,2^r,2^r); compare the Edel-Rains-Sloane paper and the tables of And and Andw mentioned here - N. J. A. Sloane, Oct 12 2001. This gives 40 in 4-D, 256 in 8-D (found also by Blokhuis), 2144 in 16-D, etc.
LINKS
A. E. Brouwer, Tables of general binary codes
A. E. Brouwer, Bounds for binary constant weight codes
Y. Edel, E. M. Rains and N. J. A. Sloane, New record kissing numbers in dimensions 32 to 128, Elect. J. Combin.
Y. Edel, E. M. Rains and N. J. A. Sloane, New record kissing numbers in dimensions 32 to 128
EXAMPLE
It is easier to take the norm to be 2. For n=2: { +-2 0, 0 +-2, +-1 +-1 }; for n=3: { 200 etc. (6) and 110 etc. (12) }; for n=4: { 2000 etc. (8), 1100 etc. (24), .5 .5 .5 .5 etc. (8) }.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Aart Blokhuis (aartb(AT)win.tue.nl), Oct 11 2001
STATUS
approved