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On the dual codes of skew constacyclic codes. (English) Zbl 1402.94108

Summary: Let \(\mathbb{F}_q\) be a finite field with \(q\) elements and denote by \(\theta : \mathbb{F}_q\rightarrow\mathbb{F}_q\) an automorphism of \(\mathbb{F}_q\). In this paper, we deal with skew constacyclic codes, that is, linear codes of \(\mathbb{F}_q^n\) which are invariant under the action of a semi-linear map \(\phi_{\alpha,\theta}:\mathbb{F}_q^n\rightarrow\mathbb{F}_q^n\), defined by \(\phi_{\alpha,\theta}(a_0,\ldots, a_{n-2}, a_{n-1}): = (\alpha \theta (a_{n-1}),\theta (a_0),\ldots,\theta (a_{n-2}))\) for some \(\alpha \in \mathbb{F}_q\setminus\{0\}\) and \(n\geq2\). In particular, we study some algebraic and geometric properties of their dual codes and we give some consequences and research results on 1-generator skew quasi-twisted codes and on MDS skew constacyclic codes.

MSC:

94B15 Cyclic codes
94B35 Decoding
12Y05 Computational aspects of field theory and polynomials (MSC2010)
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)

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References:

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