Author: Stan Eisenstat
Subject: Re: [Cs323] Syndrome for one bit vs two bit error
Date: Monday, 12 Oct 2020, 07:23:04

    > Message Posted By: Unknown
    >
    > Sorry -- it is late. I have a quick question. In your notes, it is stated
    > that for one-bit errors the syndrome is the index of the error, while for
    > two-bit errors the syndrome is non-zero. How exactly do we distinguish the
    > one-bit error and the two-bit error from a non-zero syndrome?

You cannot in general (the exception is a syndrome that
cannot be an index; e.g., 1111 when there are 8 data
bits and 4 parity bits).  Thus the Hamming code can
EITHER correct single-bit errors OR detect single- and
double-bit errors, but not both.

The extra overall parity bit lets you distinguish
between the cases and thus correct single-bit errors
and detect double-bit errors.

--Stan-