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abstract: 'Let $\mathbb{F}_q$ be a finite field with $q$ elements and denote by $\theta : \mathbb{F}_q\to\mathbb{F}_q$ an automorphism of $\mathbb{F}_q$. In this note, we deal with skew constacyclic codes, i.e. linear codes of $\mathbb{F}_q^n$ which are invariant under the action of a semi-linear map $T:\mathbb{F}_q^n\to\mathbb{F}_q^n$, defined by $T(a_0,...,a_{n-2}, a_{n-1}):=(\alpha a_{n-1},a_0,...,a_{n-2})$ for some $\alpha\in\mathbb{F}_q-\{0\}$ and $n\geq 2$. In particular, we study some algebraic and geometric properties of their dual codes and we give some Magma Programs as applications of the main theoretical results.'
address: ' Departamento de Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile'
author:
- 'Alexis E. Almendras Valdebenito and Andrea Luigi Tironi'
---

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Introduction {#introduction .unnumbered}
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Let $\mathbb{F}_q$ be a field with $q$ elements. A linear code $\mathcal{C}$ of length $n$ and dimension $k$, called an $[n,k]_q$-code, is a $k$-dimensional subspace of $\mathbb{F}_q^n$. Moreover, an $[n,k]_q$-code $\mathcal{C}$ with minimum Hamming distance $d:=d(\mathcal{C})$ is denoted as an $[n,k,d]_q$-code. A fundamental problem in Coding Theory is that of optimizing one of the parameters $n, k, d$ for given the other two. If $d_q(n,k)$ denotes the largest value of $d$ for which an $[n,k,d]_q$-code exists, we call an $[n,k,d_q(n,k)]_q$-code simply an optimal code. It is well known that 