17. Suppose we want to issue ID numbers, in the form of strings of n bits, to 1000 people, using a 1-error-correcting code. What is the least value of n for which this may be possible?20. An r-error- correcting code CBn is said to be perfect if the neighbourhoods Nr(c) exactly cover Bn - that is, every word in Bn is in precisely one Nr(c). Show that if r=1 and such a code exists, then n must be of the form 2m1. [See also Section 9.1.].