Introduction to Cryptography with Coding Theory, 3rd Edition

24.2 Error Correcting Codes

A sender starts with a message and encodes it to obtain codewords consisting of sequences of symbols. These are transmitted over a noisy channel, depicted in Figure 24.1, to the receiver. Often the sequences of symbols that are received contain errors and therefore might not be codewords. The receiver must decode, which means correct the errors in order to change what is received back to codewords and then recover the original message.

Figure 24.1 Encoding and Decoding

Figure 24.1 Full Alternative Text

The symbols used to construct the codewords belong to an alphabet. When the alphabet consists of the binary bits 0 and ...