Linear-recurrent binary error-correcting codes for memoryless channels

This paper concerns the analysis of recurrent-type, parity-check, error-correcting codes for memoryless, binary symmetric channels. These codes are defined to consist of message sequences augmented by insertions of successive parity digits every successive message digits. An analysis framework is established for the codes which consists mainly of a parity check matrix and a message difference vector . Within this framework, a decoding scheme is developed which renders the codes capable of correcting any set of errors in successive digit blocks of coded message sequence, where is maximized over all parity-check codes having the same redundancy ratios and maximal lengths of dependence among their digits. An example is given of a linear-recurrent code which has a lower probability of error than the best comparable block code, and several outstanding problems are discussed.