n-dimensional codes for detecting and correcting multiple errors0
By Morris Rubinoff
Communications of the ACM,
Vol. 4 No. 12, Pages 545-551
The paper introduces a new family of codes for detecting and correcting multiple errors in a binary-coded message. The message itself is arranged (conceptually) into a multidimensional rectangular array. The processes of encoding and error detection are based upon parity evaluations along prescribed dimensions of the array. Effectiveness of the codes is increased by introducing a “system check bit”, which is essentially a parity check on the other parity bits. Only three-dimensional codes are discussed in this paper, with parity evaluations along the horizontal, the vertical, and one main diagonal. However, the family of codes is not restricted to three dimensions, as evidenced by the discussion by Minnick and Ashenhurst on a similar multidimensional single-bit selection plan used for another purpose . A four-dimensional code, correcting three and detecting four errors, has been developed; the extension to higher-dimensional codes with greater correction power is straightforward.
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