Self-orthogonal codes are a subclass of linear codes that are contained within their dual codes. Since self-orthogonal codes are widely used in quantum codes, lattice theory and linear complementary dual (LCD) codes, they have received continuous attention and research. In this paper, we construct a class of self-orthogonal codes by using the defining-set approach, and determine their explicit weight distributions and the parameters of their duals. Some considered codes are optimal according to the tables of best codes known maintained at \cite{Grassl} and a class of almost maximum distance separable (AMDS) codes from their duals are obtained. As applications, we obtain a class of new quantum codes, which are MDS or AMDS according to the quantum Singleton bound under certain conditions. Some examples show that the constructed quantum codes have the better parameters than known ones maintained at \cite{Bierbrauer}. Furthermore, a new class of LCD codes are given, which are almost optimal according to the sphere packing bound.

翻译：自正交码是线性码的一个子类，其包含于其对偶码中。由于自正交码在量子码、格理论及线性互补对偶码中具有广泛应用，持续受到关注与研究。本文利用定义集方法构造了一类自正交码，确定了其精确的重量分布及对偶码参数。根据\cite{Grassl}维护的已知最优码表，部分所构造码达到最优；同时由其偶码得到一类几乎极大距离可分码。在应用方面，我们获得了一类新的量子码，其在特定条件下根据量子Singleton界达到MDS或AMDS标准。若干算例表明，所构造量子码的参数优于\cite{Bierbrauer}中记录的已知结果。此外，本文还给出了一类新的线性互补对偶码，根据球包界判定其几乎达到最优。