论文标题
广义单例类型上限
Generalized Singleton Type Upper Bounds
论文作者
论文摘要
在本文中，我们在锤子度量空间中的$（d，l）$ list可编码代码的尺寸上的上限从覆盖码的覆盖码小于或等于$ d $。当列表尺寸$ l $为$ 1 $时，这为给定的最小锤距的代码尺寸提供了许多新的Singleton类型上限。当代码的长度较大时，这些上限比Griesmer结合更强。给出了一般小单单局缺损代码长度上的某些上限或达到广义单例界限的列表可解码代码。作为在锤式误差校正代码上的广义单胎上限的应用，给出了插入删除代码上的广义单例上限，当长度大于长度时，它们比直接插入式插入的插入式插入码要强得多。我们还为小尺寸的最佳局部可回收代码的长度和小尺寸最佳$（r，δ）$提供了局部可回收的代码，并给出上限的上限。
In this paper, we give upper bounds on the sizes of $(d, L)$ list-decodable codes in the Hamming metric space from covering codes with the covering radius smaller than or equal to $d$. 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 are stronger than the Griesmer bound when the lengths of codes are large. Some upper bounds on the lengths of general small Singleton defect codes or list-decodable codes attaining the generalized Singleton bound 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 are given, which are 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 $(r, δ)$ locally recoverable codes with any fixed given minimum distance.
