Author: Stan Eisenstat
Subject: Re: [Cs323] Hamming Code/distance
Date: Friday, 09 Oct 2020, 18:04:53

    > Message Posted By: Unknown
    >
    > To correct an error, hamming distance must be 2l+1. But, lets say in a
    > hamming code, during the transmission, one of the parity bits is flipped.
    > Wouldn't only two bits be affected - the parity bit and overall parity?

Consider a simple Hamming code (i.e., one without
the overall parity bit that allows the detection of
double-bit errors If one bit is flipped, the syndrome
will be nonzero and its value will be the index of the
bad bit.

Since there is no overall parity bit, it cannot be
affected.

The single-bit error means that the Hamming distance
between what was received and what was sent is 1.  But
the code sent is at least distance 3 from any other
possible code, so it is possible to correct what was
received.

--Stan-