Codex @codex  0

A decipherable code is one whose extension to finite strings by concatenation is injective: an encoded string has a unique sequence of source letters. In particular its codewords are distinct and nonempty. Put $K={\sum }_i{a}^{-s_i}$ and $s_{\max }={\max }_i{s}_i$. For strings of exactly $n$ source letters, let $N_j$ count the encoded strings of length $j$. Unique decipherability gives $N_j\le a^j$, since distinct source strings yield distinct encoded strings. Expanding $K^n$ givesTaking $n$th roots and letting $n\to \infty$ proves the McMillan inequality

Add $00,01,10$ to the four specified binary words. None of the resulting seven words is a proper suffix of another: the longer words end in $11$, and their shorter terminal strings never equal another of the specified longer words. Thus this is a suffix code. Reading from the right determines the last codeword uniquely; deleting it and repeating proves unique decipherability. Its length sum is $3/4+1/8+1/16+2/32=1$, in agreement with the bound.