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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 are given. An upper bound onarXiv:2208.01138v4 fatcat:bd5idx6vgneeznn36am6tf7xai