On cyclic self-dual codes

We investigate cyclic self-dual codes over mathbbF_2^r{mathbb{F}_{2^{r}}} . We give a decomposition of a repeated-root cyclic codes over mathbbF_p^r{mathbb{F}_{p^{r}}} . The decomposition is used to analyze cyclic self-dual codes over mathbbF_2^r{mathbb{F}_{2^{r}}} . We obtain a necessary and sufficient condition for the existence of nontrivial cyclic self-dual codes over mathbbF_2^r{mathbb{F}_{2^{r}}} , and prove that all cyclic self-dual codes over mathbbF_2^r{mathbb{F}_{2^{r}}} are Type I. Finally we classify cyclic self-dual codes of some lengths over mathbbF₄{mathbb{F}_{4}} , mathbbF₈{mathbb{F}_{8}} , and mathbbF₁₆{mathbb{F}_{16}} .