Would it be feasible to give two parties a seed to generate random numbers? So that when they want to send data to each other they send the correction on the random number generated?
The random number generated: 110001
Data you want to send: 101010
Correction you send(with 1 good and 0 false): 100100
Obviously, this could only work in a small group (with trusted members) and the seed would need to be stored safely. Other than this could this system actually have a use?