Appendix F - Classical Error Correcting Codes

Classical error correcting codes are in use in a wide variety of digital electronics and other classical information systems. It is a good idea to learn some of the basic coding methods and simple examples of classical error correcting codes in order to understand the (slightly) more complicated quantum error correcting codes.

One example was already given in Chapter 7. This was the three-bit redundant encoding

	$0_{L}=000,\;\;\;{\mbox{ and }}\;\;\;1_{L}=111,\,\!$	(F.1)

where the subscript $L\,\!$ is used to denote a "logical" state, that is, one which is encoded.

$\,\!$