[[Coding theory MOC]]
# Automorphism group of a linear code

Let $\mathcal{C} \leq \mathbb{K}_{q}^n$ be a [[linear code]]. 
The **automorphism group** $\Aut \mathcal{C}$ is the [[group]] of all [[Linear equivalence of codes|linear equivalences]] of $\mathcal{C}$ with itself, #m/def/code
i.e. [[monomial transformation|monomial transformations]] $\varphi : \mathbb{K}_{q}^n \to \mathbb{K}_{q}^n$ such that $\varphi(\mathcal{C}) = \varphi(\mathcal{C})$,


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