In a good cryptographic system, changing one bit in the ciphertext changes enough bits in the corresponding plaintext to make it unreadable. Therefore, we need a way of detecting and correcting errors that could occur when ciphertext is transmitted.
Many noncryptographic situations also require error correction; for example, fax machines, computer hard drives, CD players, and anything that works with digitally represented data. Error correcting codes solve this problem.
Though coding theory (communication over noisy channels) is technically not part of cryptology (communication over nonsecure channels), in Section 24.10 we describe how error correcting codes can be used to construct a public key cryptosystem.