In this paper, we first generalize the class of linear codes by Ding and Ding (IEEE TIT, 61(11), pp. 5835-5842, 2015). Then we mainly study the augmented codes of this generalized class of linear codes. For one thing, we use Gaussian sums to determine the parameters and weight distributions of the augmented codes in some cases. It is shown that the augmented codes are self-orthogonal and have only a few nonzero weights. For another thing, the locality of the augmented codes is proved to be 2, which indicates the augmented codes are useful in distributed storage. Besides, the augmented codes are projective as the minimum distance of their duals is proved to be 3. In particular, we obtain several (almost) optimal linear codes and locally recoverable codes.

翻译：本文首先推广了Ding和Ding（IEEE TIT, 61(11), pp. 5835-5842, 2015）提出的线性码类，然后主要研究该推广线性码类的增广码。一方面，我们利用高斯和确定某些情况下增广码的参数与重量分布，结果表明增广码是自正交的且仅有少数几个非零重量。另一方面，我们证明了增广码的局部性为2，这表明其在分布式存储中具有应用价值。此外，由于对偶码的最小距离被证明为3，增广码是射影的。特别地，我们得到了若干（几乎）最优线性码与局部可恢复码。