$$\pmb {{\mathbb {F}}}_q$$ F q -Linear skew cyclic codes over $$\pmb {{\mathbb {F}}}_{q^2}$$ F q 2 and their applications of quantum codes construction

In this paper, we study the structure of $${\mathbb {F}}_q$$ -linear skew cyclic codes over $${\mathbb {F}}_{q^2}$$ . Some good $${\mathbb {F}}_q$$ -linear skew cyclic codes over $${\mathbb {F}}_{q^2}$$ are constructed. Moreover, as an application, some good quantum codes are obtained by $${\mathbb {F}}_q$$ -linear skew cyclic codes over $${\mathbb {F}}_{q^2}$$ .