In this paper, we study a class of special linear codes involving their parameters, weight distributions, and self-orthogonal properties. On one hand, we prove that such codes must be maximum distance separable (MDS) or near MDS (NMDS) codes and completely determine their weight distributions with the help of the solutions to some subset sum problems. Based on the well-known Schur method, we also show that such codes are non-equivalent to generalized Reed-Solomon codes. On the other hand, a sufficient and necessary condition for such codes to be self-orthogonal is characterized. Based on this condition, we further deduce that there are no self-dual codes in this class of linear codes and explicitly construct two classes of almost self-dual codes.

翻译：本文研究了一类特殊线性码的参数、重量分布及自正交性质。一方面，我们证明此类码必为最大距离可分（MDS）码或近MDS（NMDS）码，并借助若干子集和问题的解完全确定了它们的重量分布。基于著名的Schur方法，我们还证明此类码与广义Reed-Solomon码不等价。另一方面，刻画了此类码为自正交码的充要条件。基于该条件，进一步推得此类线性码中不存在自对偶码，并显式构造了两类几乎自对偶码。