In this paper we give upper bounds on the sizes of $(d, L)$ list-decodable codes in the Hamming metric space from various covering codes with the covering radius $d$. When the list size $L$ is $1$, this gives many new Singleton type upper bounds on the sizes of codes with a given minimum Hamming distance. These upper bounds for codes are tighter than the Griesmer bound when the lengths of codes are large. Some upper bounds on the lengths of general small Singleton defect codes are given. As an application of our generalized Singleton type upper bounds on Hamming metric error-correcting codes, the generalized Singleton type upper bounds on insertion-deletion codes is given. Our this upper bound is much stronger than the direct Singleton bound for insertion-deletion codes when the lengths are large. We also give upper bounds on the lengths of small dimension optimal locally recoverable codes and small dimension optimal $(r, \delta)$ locally recoverable codes with any fixed given minimum distance.
翻译：在本文中,我们给出了包含半径为$1美元的各种覆盖代码中(d、L)美元列表-可脱钩的标码大小的上限。 当列表大小为$L美元时, 给出了许多新的单方字型的标码大小的上限, 并设定了一个最小的标码距离。 当代码长度较大时, 这些代码的上限比Griesmer所约束的码要紧。 给出了普通小型单吨缺陷代码长度的一些上限。 作为我们通用的单方字型单方字的通用标码的上限, 给出了插入删除代码中通用单方字型的上限。 我们的这一上限框比在长度较大时用于插入删除代码的直接单方字型要强得多。 我们还给出了小维最佳本地可回收代码长度的上限, 和小维的本地可回收代码的最小值为$(r,\delta)$(l)$(r, delta)$(ta) 。
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