An encoder is disclosed which includes circuitry and memory. Using the memory, the circuitry, in a first operating mode, derives first motion vectors for a first block obtained by splitting a picture, and generates a prediction image corresponding to the first block, with a bi-directional optical flow flag settable to true, and by referring to spatial gradients of luminance generated based on the first motion vectors. Using the memory, the circuitry, in a second operating mode, derives second motion vectors for a sub-block obtained by splitting a second block, the second block being obtained by splitting the picture, and generates a prediction image corresponding to the sub-block, with the bi-directional optical flow flag set to false.