Verify that over Z3 g(x) = x5 + x4 + 2x3 + x 2 + 2 is a divisor of xl! - 1.

Let C be the cyclic ternary [11, 6] code (g(x)).

Given that d( C) = 5, use error trapping to decode the received word 20121020112. What proportion of errors of weight 2 are not correctable by this method?