In Friday’s lecture, we started by wondering if the GV bound is tight for *binary* codes? We looked at the special case of odd **constant** distance (i.e. ). We revisited some of the bounds for the constant distance regime. In particular, we saw that the GV bound in this case states

On the other hand, the Hamming bound states:

For , we had already seen the Hamming code, which meets the Hamming bound (and hence, beats the GV bound). In the lecture we studied the code, which is the subfield sub-code of the RS code. We argued in the lecture that

In fact, it can be show that

For the proof of the above see these lecture notes from Madhu Sudan‘s coding theory course (the argument we used to show the weaker lower bound on is also from the same notes).

### Like this:

Like Loading...

*Related*

## Leave a Reply