A linear code is said to be self-orthogonal if it is contained in its dual. Self-orthogonal codes are of interest because of their important applications, such as for constructing linear complementary dual (LCD) codes and quantum codes. In this paper, we construct several new families of ternary self-orthogonal codes by employing weakly regular plateaued functions. Their parameters and weight distributions are completely determined. Then we apply these self-orthogonal codes to construct several new families of ternary LCD codes. As a consequence, we obtain many (almost) optimal ternary self-orthogonal codes and LCD codes.

翻译：线性码若包含于其对偶码中，则称为自正交码。自正交码因其在构造线性互补对偶（LCD）码和量子码等重要应用而备受关注。本文利用弱正则平台函数构造了若干类新的三元自正交码族，并完全确定了它们的参数和重量分布。进而将这些自正交码应用于构造若干类新的三元LCD码族。作为结果，我们获得了大量（几乎）最优的三元自正交码和LCD码。