Let's say you have $n$ symbols. You can encode a $\log_2(n!)$-bit message by permutating the symbols. I will call this a permutation code (if you have seen this concept before, I would love to see a reference).
Let's say we are encoding a message with $k<\log_2(n!)$ bits. It is possible to add error correction. One way is to simply add any old error correction scheme to the string before applying the permutation code. I'm wondering if there is a way that is optimal for permutation codes.
In particular, is there some way of doing a permutation coding that is resistant to transpositions (in terms of error detection and correction)? I want something that will tolerate up to $t$ transpositions of adjacent symbols.