EXAMPLE 1 An Error-Correcting Code

Assume that we want to send the message 1001. We append extra information to this message with the aid of the diagram in Figure 17.1. Begin by placing the four message digits in the four overlapping regions I, II, III, and IV, with the digit in the first position (starting at the left of the sequence) in region I, the digit in the second position in region II, and so on. For regions V, VI, and VII, assign 0 or 1 so that the total number of 1s in each circle is even (see Figure 17.2). The encoded message 1001101 is obtained by reading the entries in regions I through VII in order.