A Class of High Rate Codes for Byte-Oriented Information Systems

In this paper we introduce a class of linear codes especially designed to provide additional error protection for data consisting of bytes all having even (or odd) parity (e.g., ASCII characters). The technique consists in adding an overall parity byte computed as a linear function of the information bytes. The linear function is designed such that the resulting codes can correct all single errors and all double errors occurring in distinct information bytes. It is shown that any code which can correct these latter mentioned error patterns has an overall length of at most 37 bytes, and a specific code of length 29 bytes is described. A practical decoding algorithm for the new class of codes is described. Finally, the performance of the codes, when used on the binary symmetric channel, is compared with that of the row-column codes for which the additional parity byte is simply the modulo-2 sum of the information bytes.