Symplectic self-orthogonal codes over finite fields are an important class of linear codes in coding theory, which can be used to construct quantum codes. In this paper, characterizations of symplectic self-orthogonal codes over finite fields Fq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F_{q}$$\end{document} are given. A necessary and sufficient condition for determining symplectic self-orthogonal codes is obtained. Several classes of symplectic self-orthogonal codes are constructed. Furthermore, the symplectic weight distributions of some new classes of binary symplectic self-orthogonal codes are completely determined.

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关于一些二进制辛自正交码

有限域上的辛自正交码是编码理论中一类重要的线性码，可用于构造量子码。在本文中，有限域上辛自正交码的表征 Fq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage {mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F_{q}$$\end{document} 给出。得到了确定辛自正交码的充要条件。构造了几类辛自正交码。此外，完全确定了一些新的二进制辛自正交码类的辛权重分布。