N-Dimensional Codes for Detecting and Correcting Multiple Errors

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 [6]. 
 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.

CACM December, 1961

Rubinoff, M.

CA611207 JB March 15, 1978  10:23 PM

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