For a minimum length code, length of symbols should be in the opposite order of the probability of the symbol occuring.

We want a instantaneous, uniquely decodable code for given set of input symbols $s_i$, along with their probabilities $p_i$.

Theorem

If $p_i$ are in descending order, then $l_i$ should be in ascending order

Proof

Suppose $p_i$ are in order, but at least one pair of $l_i$ are not.

Their contribution to the average length $L$ is

After interchanging the two codes

Difference is

One of these two is factors is negative, hence the difference is negative. So if we interchange, we get a smaller contribution to the average length $L$. This means that in a minimum length code, the two running inequalities must be true.

Source: The Art of Doing Science and Engineering: Learning to learn