Damnit, that ternary system needs more theory than I expected. I now have to use "higher math" to get things done.

More formally I have defined 2 operations on a ternary marker:

• rotation : maps 012 to 201 (circular shift by one position)
• swap : maps 012 to 021 (any 1 becomes 2 and vice versa)

And I had found the fortunate identity :

ID = swap(swap) = swap(rot(swap(rot)))

Thus Rot-¹ = swap(rot(swap))  as in the 1st version, which worked with the first ternary version.

 Now I need to work that further so it can handle rot combined with swap. I can't have 2 rot because it's too long so I can't use ID = rot(rot(rot)), only 2 rot at most are possible (one in sender, the other in receiver).

• Encoding side :
  • S=0,O=0 => ID  : 012 => 012
  • S=0,O=1 => rot  :  012 => 201
  • S=1,O=1 => swap(rot)  : 012 => 102...
• Decoding side :
  • S=0,O=0 => ID :  012 => 012
  • S=0,O=1 => swap(rot(swap)) : 201 => 102 => 
  • S=1,O=1 => swap(rot) ?   102

...

It doesn't feel very right because rot^-1 = rot(rot) = 120 : the position of the 0 should be shifted by each rot operation.

___________________________________________________________

The "solution" looks like "yet another adder", but an unusual one : mod 3.