Hi,

I have a test soon about a lot of things, including a part with error-correction Hamming codes.

I thought I had enough things to work on on my notes, but now it looks like I was wrong

I have this exercise (roughly translated from french) :

A transmission has been received, and the message is the following : 101111001101110

1) Determine the syndrome [word].

2) What's the 11-bit message that has been sent ?

So basically, I believe the structure of the message is :

1011110

**0**110

**1**1

**1****0**_______P

_{3}__P

_{2}_P

_{1}P

_{0}(non-bold are the actual content, with maybe an error ? ; bold are parity-check bits)

I believe the message contains an error because P3 is 0 while there are 5 "1" at its left, which would have given a "1" for P3.

How do I determine the syndrome ?

I've looked on wikipedia and such, and it looks like I have to multiply 2 vectors (one being the matrix H of the parity bits things, and the other one being the vector of the whole message), to find a syndrom vector indicating the error position ?

I'm not too sure how to do that in my case but here's what I tried :

which gave me [[5][6][7][5]].

But I rememebered that it's not really a multiplication here, since we have to replace the additions by a parity-check operation which turns out to be a xor. -_-

Do you have an easy way (or rather, not time-consuming) to know what bit is wrong ?

I'm sure I could read a lot more lessons online and eventually find what I need but maybe you guys will know directly what to tell me

Thanks !

Edit : see 3rd post in this topic.