Linear codes for single error correction in symmetric and asymmetric computational processes
A. J. Bernstein, Wan Kim · IEEE Transactions on Information Theory · 1962
A linear coding scheme for the correction of all possible single errors during arithmetic operations on binary number representations is discussed. The coded form of a numberkis the binary representation of the numberkt, wheretis a positive integer. The code corrects all errors of the form\pm2^i, whereiis less thann, the number of digits in the code words. The problem of determining the largest numberkwhich may be encoded for a particular value oftis discussed. It is also shown that as the number of arithmetic operations to be performed increases, the use of this coding scheme becomes more significant in improving the reliability of the computational unit. An asymmetric process (in which only 1-errors or only O-errors are to be corrected) is also investigated and compared with the symmetric process.