A systematic (16, 8) code for correcting double errors, and detecting random triple errors

We examine several systematic (16,8) codes capable of double error correction (DEC) and triple adjacent error detection. In particular, we examine a linear version of the Nordstrom-Robinson (NR) code in the light of new findings by Hammons (see IEEE Trans. Inform. Theory, vol.40, p.301, 1994) and others, and compare it with the (16, 8) code by Gulliver and Bhargava (see EEE Trans. Comp, vol.42, no.1, p.109, 1993). The NR code is non-linear, and because of its lack of algebraic structure, does not lend itself easily to use in its original form. However, it is now known that the NR code is the binary image of the octacode, and the octacode is a linear code. As a result of these new insights, we show that the NR code can be used to correct double errors (DEC), and simultaneously detect triple random errors (TED). These results are compared to the Gulliver and Bhargava (16, 8) code and summarized. We show that the linear form of the NR code can be decoded efficiently