## Codes

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.
$D = \{x \in \mathbb{F}^n_q : \forall c \in C = 0\}$ with $ = \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