1. A moving picture encoding device for encoding a moving picture constituted of a time sequence of frame pictures by motion compensation, the device comprising: a reference picture generation section configured to generate a plurality of different reference pictures, by executing filtering, through a filter that has a plurality of different pass bands a single reference frame picture; a 3-dimensional motion vector generation section configured to generate a 3-dimensional motion vector, by generating a three term vector including space resolution and a two dimensional motion vector, wherein the space resolution is an identifier of the filter; a motion compensation section configured to calculate a motion compensation value for a predetermined area to be encoded, by using a generated reference picture; and a transmission section configured to transmit a combination of the 3-dimensional motion vector and information indicating the motion compensation value.