Thanks for engaging, and good questions. Please help me firm up the definitions.
How do you measure the difference between two orderings? As the number of inversions?
Number of inversions probably makes sense, but I guess it depends. If we come up with some clever way of doing this (e.g. with a non-standard deck of cards) then maybe there is some other measure we could use?
And what are you trying to maximize here? The number of cards you can lose? Can any subset of card indices be lost?
It would be great if some subset of the larger M-card deck (M = 54 in the example) could be lost and yet still be able to reconstruct the data where the data in the example is a number between 0 and factorial(N) where N = 13. I was representing that number as a permutation of 13 objects, but I suppose that part is not very important.
Think about data as being the entropy+checksum for a bip39 seed. What I want is definitions for encode and decode such that:
encode(data) = f
decode(g) = data
where f and g are not equal, but f and g are permutations of {1,2,3,4,...,M}.
M-carddeck (M = 54in the example) could be lost and yet still be able to reconstruct thedatawhere thedatain the example is a number between0andfactorial(N)whereN = 13. I was representing that number as a permutation of13objects, but I suppose that part is not very important.dataas being the entropy+checksum for a bip39 seed. What I want is definitions forencodeanddecodesuch that:fandgare not equal, butfandgare permutations of {1,2,3,4,...,M}.