Linear equivalence of codes

MacWilliams theorem

Let 𝜑 :C →C′ be a linear isomorphism between [𝑛,𝑘] codes C,C′. Then if the generalized Hamming weight wt𝑡⁡(D) =wt𝑡⁡(𝜑(D)) for every 𝑡-dimensional linear subcode D ≤C, then 𝜑 is a Linear equivalence of codes.¹

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