The augmented codes of a family of linear codes with locality 2
CoRR(2024)
Abstract
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.
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