1. A picture coding device adapted to code each of blocks obtained by partitioning each picture of moving pictures, by using motion vectors, comprising: an acquisition unit configured to acquire coding information on a plurality of reference block candidates for the block subject to coding; a first mode detection unit configured to construct, in a first inter prediction mode that uses information on a motion vector provided in the coding information of a reference block identified by an index, a first candidate list from the plurality of reference block candidates in accordance with a first predetermined order, to assign indices for identifying reference block candidates added in the first candidate list, and to output the indices of the plurality of reference block candidates; a second mode detection unit configured to construct, in a second inter prediction mode that uses a motion vector predictor difference between a motion vector predictor based on information on a motion vector provided in the coding information of a reference block identified by an index and a motion vector of the block subject to coding, a second candidate list from the plurality of reference block candidates in accordance with a second predetermined order, to assign indices for identifying reference block candidates added in the second candidate list, and to output the indices of the plurality of reference block candidates and the motion vector difference; a prediction method decision unit configured to decision a reference block and an inter prediction mode for each block subject to coding, based on outputs from the first and second mode detection units; and a bitstream generation unit configured to code the index of the reference block decisioned by the prediction method decision unit, prediction mode information indicating the inter prediction mode decisioned by the prediction method decision unit, and the motion vector difference corresponding to the reference block, the motion vector difference being coded when the prediction method decision unit decisions on the second inter prediction mode, wherein the first and second mode detection units use a plurality of common blocks as the plurality of reference block candidates, and wherein the first predetermined order of arranging the reference block candidates in the first candidate list constructed by the first mode detection unit differs from the second predetermined order of arranging the reference block candidates in the second candidate list constructed by the second mode detection unit.