MacWilliams theorem

Let $𝜑 : C \to C'$ be a linear isomorphism between [[Linear code| $[𝑛, 𝑘]$ codes]] $C, C'$ . Then if the generalized Hamming weight $w t 𝑡 (D) = w t 𝑡 (𝜑 (D))$ for every $𝑡$ -dimensional linear subcode $D \leq C$ , then $𝜑$ is a Linear equivalence of codes.¹