Today, 01:17
Here is a video using the 9 numbers. Where the entropy is changed by using the transform. It uses the same transform as the example above. Please note the toggle bit is needed to note if the stream starts with a odd or even number. The stream is also changed from high to low entropy. In the next video I will show how the decode works. It is a simple process. perhaps you have already figured it out. If you reverse the of (0,0,1,2,5,6,7,3,5) you end up with the original of (8,1,3,4,6,2,7,9,5). Because of the key of (3,4,5,6,7,8,9,0,1,2) any number that starts even will end in 0, in 4, or less than 4 steps, and any number that starts in an odd number will end in a 1, in less than for steps.
Using another method it is possible to change the entropy even more where you can use a huffman code.
You do not change the key, (however you can use various keys multi key encryption but that is another topic) you always use the same key. The key though, becomes part of the plaintext or in this case part of the stream you are compressing. The new permutation is very subjective. Depending on the key you can produce all permutation of length n counting in base n or filter the results so the permutations only progress through specific numbers in this case if it is an even number the permutation output will always start with (9,7,5,3,1) if it is even (8,6,4,2,0) Then you subtract a 0 or subtract a 1. Inversely you add a 1 or a 0.
Video showing transform of number from high entropy to low.