Let $I = i : x_i \neq z_i$, $J = i : x_i \neq y_i$, and $K = i : y_i \neq z_i$. Note that $I \subseteq J \cup K$.
: For complex polynomials (common in BCH or Goppa codes), use software like MATLAB or Python's galois library to verify your manual calculations. Solution Manual- Coding Theory by Hoffman et al. - PubHTML5
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Then, $|\mathcalC| \cdot \sum_i=0^t \binomni (q-1)^i \leq q^n$, where $t = \lfloor \fracd-12 \rfloor$. Let $I = i : x_i \neq z_i$,
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The generator matrix is $G = \beginpmatrix 1 & 1 & 1 \endpmatrix$. Solution Manual- Coding Theory by Hoffman et al
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