Linear code

Linear equivalence of codes

Let C,D ≤𝕂𝑛𝑞 be linear codes. Then C,D are said to be linearly equivalent iff there exists a monomial transformation 𝜑 :𝕂𝑛𝑞 →𝕂𝑛𝑞 such that 𝜑(C) =D.¹ code Equivalently, generator matrices 𝐺,𝐺′ of C,D respectively are related by permutation and rescaling of columns.

Properties

• MacWilliams theorem

See also

• Automorphism group of a linear code

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Footnotes

1. 2011. On the equivalence of linear codes ↩