Size of 1-Error-Detecting Codes in Three Interactive Transmissions

This paper considers the error-detecting codes between two nodes. There are three transmissions between these two nodes: node A and node B. The first transmission can transmit one symbol within the alphabet {0, 1, ... , q₁-1} from node A to node B; the second transmission can transmit one symbol within the alphabet {0, 1, ... , q₂-1} from node B to node A; and the third transmission can transmit one symbol within the alphabet {0, 1, ... , q₃-1} from node A to node B. One of the three transmissions may be erroneous. We prove that the maximum size of all 1-error-detecting codes over these three transmissions is min{q₁, q₂(q₃-1)}.