Erschienen in:
20.01.2020 | Original Paper
Construction of new quantum codes derived from constacyclic codes over \({\mathbb {F}}_{q^2}+u{\mathbb {F}}_{q^2}+\cdots +u^{r-1}{\mathbb {F}}_{q^2}\)
Erschienen in: Applicable Algebra in Engineering, Communication and Computing | Ausgabe 5/2021
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Let \(R={\mathbb {F}}_{q^2}+u{\mathbb {F}}_{q^2}+\cdots +u^{r-1}{\mathbb {F}}_{q^2}\) be a finite non-chain ring, where q is a prime power, \(u^{r}=1\) and \(r|(q+1)\). In this paper, we study u-constacyclic codes over the ring R. Using the matrix of Fourier transform, a Gray map from R to \({\mathbb {F}}_{q^2}^{r}\) is given. Under the special Gray map, we show that the image of Gray map of u-constacyclic codes over R are cyclic codes over \({\mathbb {F}}_{q^2}\), and some new quantum codes are obtained via the Gray map and Hermitian construction from Hermitian dual-containing u-constacyclic codes.
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