On Jul 15, 2018, at 8:47 AM, Joerg Sonnenberger <jo...@bec.de> wrote:
> On Sat, Jul 14, 2018 at 05:24:26PM -0600, Warren Young wrote:
>> On Jul 14, 2018, at 2:18 PM, Joerg Sonnenberger <jo...@bec.de> wrote:
>>> On Fri, Jul 13, 2018 at 03:27:14PM -0600, Warren Young wrote:
>>>> For example, 100 a’s requires a 7-bit run-length plus zero bits for our
>>>> only code point
>>> You need more than zero bits to encode the original a though.
>> There’s only one letter in this alphabet, so all we need is a run length
>> to say how many of them there are in our message.
> You are kind of making my point for me. You are adding a priori
> knowledge of a single letter alphabet in a context where this assumption
> makes no natural sense. By that line of reasoning, you can also assume
> knowledge that passwords are always a multiple of size n and the entropy
> would be near zero…

I’m taking inspiration from Huffman coding here, so you actually need 7 bits 
for the length prefix + sizeof(dictionary_with_one_entry).
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