If there is a binary (n, M, d) code, show that there is a binary (n -

1, M', d' ) code with M' ~ ~ and d' ~ d.

[Hint: At least half the words of the (n, M, d) code must start with the same symbol. What is the result of deleting this symbol from just these words?]

Deduce that A2 (n, d) ::; 2A2 (n - 1, d).