Recall that the dot product u · v of two vectors u = (u1, u2, . . . , un) and v = (v1, v2, . . . , vn) from Fn is
u 1 v 1 + u2v2 + · · · · 1 unvn
(where the addition and multiplication are those of F). Let C be an (n, k) linear code. Show that
is an (n, n - k) linear code. This code is called the dual of C.
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