Summary: IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 43, NO. 5, SEPTEMBER 1997 1619
Fig. 2. Y : the domain of unrestricted codes.
where () is the best upper bound on the rate of an unrestricted
code as a function of :
III. CONCLUSION AND OPEN PROBLEMS
We have geometrically characterized the domain of linear and
unrestricted binary codes in the (; ) plane. For > 1=2 it might
be worth shelling the domain according to the size of the code
M 6; 7; 1 1 1 : A similar study for q-ary codes for q > 2 would
also be of interest.
The authors wish to thank A. Lobstein and the anonymous referees
for many useful comments and suggestions. P. SolŽe would like to
thank R. Moore for help with preparing the figures using the XYPic
system developped at Macquarie University.
 V. M. Blinovskii, "Lower asymptotic bound on the number of linear
code words in a sphere of given radius in Fn
q ," Probl. Pered. Inform.,
vol. 23, pp. 5053, 1987. English translation in: Probl. Inform. Transm.,