We demonstrate the existence of Euclidean and Hermitian LCD codes over finite fields with various parameters. In addition, we provide a method for constructing multiple Hermitian LCD (self orthogonal, self dual) codes from a given Hermitian LCD (self orthogonal, self dual) code, as well as a method for constructing Euclidean (Hermitian) LCD codes with parameters $[n+1, k+1]$ and $[n,k+1]$ from a given Euclidean (Hermitian) LCD code with parameters $[n,k]$ over finite fields. Finally, we provide some findings on $\sigma$-LCD codes over finite fields.
翻译：此外,我们提供了一种方法,用以根据给定的埃米蒂亚LCD(自正反向、自双向)代码构建多个埃米蒂亚LCD(自正反向)代码,并用一个参数 $n+1, k+1美元和 $ $n, k+1美元来构建欧几里底亚LCD(赫米蒂亚) LCD(自正反向、自双向)代码,以及用参数 $n+1美元和 $n, k+1美元来构建欧几里底亚LCD(自上式)代码的方法。 最后,我们提供了对限定域的$\西格美-LCD代码的一些结论。
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