1. An encoding apparatus comprising: a determination unit that (a) determines whether or not an image corresponding to a target block including pixels is a low frequency band image, and (b) determines whether or not the image corresponding to the target block includes a gradation image if the image corresponding to the target block is the low frequency band image; and an encoding unit that performs an encoding process of using an intra-prediction coding to encode the target block, wherein the target block is encoded by using at least one of a first block size, a second block size, and a third block size if the image corresponding to the target block is not the low frequency band image, wherein the target block is encoded by using the third block size prior to the first block size and the second block size if the image corresponding to the target block is the low frequency band image and includes the gradation image, wherein the target block is encoded by using the first block size prior to the second block size and the third block size if the image corresponding to the target block is the low frequency band image and does not include the gradation image, wherein the third block size is smaller than the second block size, and the second block size is smaller than the first block size, and wherein at least one of the determination unit and the encoding unit has a hardware structure.