Hackett's soft decision decoding algorithm on extended golay codes

Hi,

I am trying to understand and implement Hackett's soft decision decoding algorithm on extended (24,12) Golay codes, but struggling to understand a few of the steps.

Link to the IEEE document:

http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=1095056&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D1095056

For instance, the steps:

- where "confidence" values of the input bit stream should be generated

- where Pmk is a bit value to be changed, but represents a sequence that causes "all possible changes to an even number of bits to occur"

- and in the hard-decision sub procedure where the syndrome vector is XOR'ed with a row of the parity matrix and represents a certain bit of the syndrome vector to be in error.

Has anybody worked with the algorithm from first principles before (to explain these steps to me), or better, could link me to discussions/coding implementations of the algorithm?

Any help would be much appreciated