In this work, we propose two criteria for linear codes obtained from the Plotkin sum construction being symplectic self-orthogonal (SO) and linear complementary dual (LCD). As specific constructions, several classes of symplectic SO codes with good parameters including symplectic maximum distance separable codes are derived via $\ell$-intersection pairs of linear codes and generalized Reed-Muller codes. Also symplectic LCD codes are constructed from general linear codes. Furthermore, we obtain some binary symplectic LCD codes, which are equivalent to quaternary trace Hermitian additive complementary dual codes that outperform best-known quaternary Hermitian LCD codes reported in the literature. In addition, we prove that symplectic SO and LCD codes obtained in these ways are asymptotically good.

翻译：本文针对由Plotkin和构造得到的线性码，提出了判别其是否为辛普利克自正交码（SO）与线性互补对偶码（LCD）的两个准则。作为具体构造，利用线性码的$\ell$-交对和广义里德-穆勒码，推导出若干类具有良好参数的辛普利克自正交码，包括辛极大距离可分码。同时，基于一般线性码构造了辛普利克LCD码。此外，我们获得了一些二元辛普利克LCD码，这些码等价于四元迹埃尔米特加法互补对偶码，其性能优于文献中报道的最佳已知四元埃尔米特LCD码。进一步地，我们证明了通过这些方法得到的辛普利克自正交码和LCD码是渐近优码。