## 李成举：The dual codes of several classes of BCH codes

：李成举 教授

A BCH code of length $n$ over $\mathbb{F}_q$ is always relative to an $n$-th primitive root of unity $\beta$ in an extension field of $\mathbb{F}_q$, and is called a dually-BCH code if its dual is also a BCH code relative to the same $\beta$.

In this talk, we will give sufficient and necessary conditions in terms of the designed distances $\delta$ to ensure that BCH codes are dually-BCH codes for primitive narrow-sense BCH codes and projective narrow-sense ternary BCH codes. In addition, the parameters of these BCH codes and their dual codes are investigated. The question as to what subclasses of cyclic codes are BCH codes is also answered to some extent. As a byproduct, the parameters of some subclasses of cyclic codes are also investigated.