MDS self-dual codes have nice algebraic structures, theoretical significance and practical implications. In this paper, we present three classes of the Hermitian self-dual (extended) generalized Reed-Solomon codes with different locators. Furthermore, we showed that when $n\geq 2q$, $q^2$-ary Hermitian self-dual GRS codes of length $n$ does not exist. And when $n\geq 2q-1$, $q^2$-ary Hermitian self-dual EGRS codes of length $n+1$ does not exist.

翻译：MDS自体代号具有良好的代数结构、理论意义和实际影响。本文用不同的定位器列出了三种等级的埃米蒂人自体(扩展的)通用Reed-Solomon代号。此外,我们还表明,当美元2Q美元、美元2Q美元、墨西哥自体双体GRS代号为美元时,不存在。当美元2Q1美元、美元2Q1美元、美米特人自体EGRS代号为n+1美元时,则不存在。