Self-orthogonal codes are of interest as they have important applications in quantum codes, lattices and many areas. In this paper, based on the weakly regular plateaued functions or plateaued Boolean functions, we construct a family of linear codes with four nonzero weights. This family of linear codes is proved to be not only self-orthogonal but also optimally or almost optimally extendable. Besides, we derive binary and ternary linearly complementary dual codes (LCD codes for short) with new parameters from this family of codes. Some families of self-dual codes are also obtained as byproducts.

翻译：自正交码因其在量子码、格点及诸多领域的重要应用而备受关注。本文基于弱正则平台函数或平台布尔函数，构造了一类具有四个非零权重的线性码。证明该类线性码不仅具有自正交性，且具备最优或近似最优的可扩展性。此外，我们从该类码中导出了具有新参数的二元及三元线性互补对偶码（简称LCD码），并作为副产品得到了若干自对偶码族。