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.
ACKNOWLEDGMENT
The authors wish to thank A. Lobstein and the anonymous referees
for many useful comments and suggestions. P. Sol´e would like to
thank R. Moore for help with preparing the figures using the XYPic
system developped at Macquarie University.
REFERENCES
[1] 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.,

Source: Almuhammadi, Sultan - Department of Information and Computer Science, King Fahd University of Petroleum and Minerals

Collections: Computer Technologies and Information Sciences