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A Systematic (12,8) Code for Correcting Single Errors and Detecting Adjacent Errors
November 1990 (vol. 39 no. 11)
pp. 1403-1404

A parity check matrix is given for a systematic (12,8) binary code which connects all single errors and detects eight of the nine double adjacent errors within any of the three 4-b nibbles. It is shown that no (12,8) binary systematic parity check code can correct all 12 single errors and simultaneously detect all nine double adjacent errors within 4-b nibbles. A (12,8) binary systematic parity check code is given that corrects all 12 single errors and simultaneously detects eight of the nine double adjacent errors within 4-b nibbles.

[1] W. W. Peterson and E. J. Weldon, Jr.,Error-Correcting Codes, 2nd ed., Cambridge, MA, MIT Press, 1972.
[2] S. Lin,An Introduction to Error-Correcting Codes. Englewood Cliffs, NJ: Prentice-Hall, 1970.
[3] R. E. Blahut,Theory and Practice of Error Control Codes. Reading, MA: Addison-Wesley, 1983.

Index Terms:
systematic (12,8) code; correcting single errors; detecting adjacent errors; parity check matrix; 4-b nibbles; systematic parity check code; error correction codes; error detection codes.
Citation:
J.W. Schwartz, J.K. Wolf, "A Systematic (12,8) Code for Correcting Single Errors and Detecting Adjacent Errors," IEEE Transactions on Computers, vol. 39, no. 11, pp. 1403-1404, Nov. 1990, doi:10.1109/12.61052
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