- Continuing with Exercise 7 of Chapter 1, compute the maximum number of strings of length at most 3 in a trinary code.
We simply calculate how many strings there are of length 1, 2 and 3 and add the numbers:
\[3^1 + 3^2 + 3^3 = 39\]
- Repeat for length at most 4.
Similar to (a):
\[3^1 + 3^2 + 3^3 + 3^4 = 120\]
- Repeat for length exactly 4, but beginning with a 0 or 1.
We have two choices for the first position (0 or 1) and 3 choices for each of the three subsequent positions:
\[2 \cdot 3^3 = 54\]