Find a similar formula for that in Theorem 4.10 for ternary codes, of the form

w(x + y) = w(x) + w(y) - f(x 0 y)

where 0 and the first + are modulo 3 multiplication and addition respectively, and f is a function to be found. [Hint: consider the number of Os, Is and 2s in x 0 y.]