Let C be the binary code of length 12 en dimension 4 of the form (abcd abcd abcd). Thus every message of lenght 4 is repeated 3 times.

Then C is has minimum distance 3.

Let D be the dual code.

$\displaystyle D = \{x \in \mathbb{F}^n_q : \forall c \in C <x,c> = 0\}$ with $\displaystyle <x,c> = \sum_i x_ic_i$

I want to show that the minimum distance of D is 2.

And determine the number of codewords with weight 2 in D.

Thanks