Nearly perfect packing codes are those codes that meet the Johnson upper bound on the size of error-correcting codes. This bound is an improvement to the sphere-packing bound. A related bound for covering codes is known as the van Wee bound. Codes that meet this bound will be called nearly perfect covering codes. In this paper, such codes with covering radius one will be considered. It will be proved that these codes can be partitioned into three families depending on the smallest distance between neighboring codewords. Some of the codes contained in these families will be completely characterized. Construction for codes for each such family will be presented, the weight distribution of codes from these families will be examined, and some codes with special properties will be discussed.

翻译：近似完美打包码是那些达到纠错码大小约翰逊上界的码。该界是对球包界的一种改进。覆盖码的一个相关界被称为 van Wee 界，达到此界的码将被称为近似完美覆盖码。本文考虑覆盖半径为1的此类码，并证明这些码可根据相邻码字间的最小距离划分为三个族系。我们将完全刻画其中部分族系所含的码，给出每个族系码的构造方法，研究这些族系码的重量分布，并讨论一些具有特殊性质的码。