1. An image coder comprising: a memory to store a reference image which is a previously decoded image; a block matching section to estimate motion vectors between an input image to be coded and the reference image, to synthesize a prediction image of the input image using the motion vectors and the reference image, and to generate a difference image by calculating a difference between the input image and the prediction image; and a multiplexer to produce coded information of the input image including information related to the difference image and the motion vectors, wherein the prediction image is synthesized by calculating intensity values at points where no pixels actually exist in the reference image by interpolation, wherein the interpolation is done using a positive rounding method or a negative rounding method when the input image is coded as a P frame, wherein the coded information of the input image coded as P frames includes information specifying the rounding method used in the interpolation, and wherein the coded information of the input images coded as I frames does not include information specifying the rounding method used in the interpolation.