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 that acquires coding information on a plurality of reference blocks for the block subject to coding; a first mode detection unit that constructs, 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 by deriving the coding information from the plurality of reference blocks in accordance with a first predetermined order, assigns first indices for identifying the coding information added in the first candidate list, and outputs the first indices; a second mode detection unit that constructs, in a second inter prediction mode that uses a motion vector 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 by deriving motion vector predictors from the plurality of reference blocks in accordance with a second predetermined order, assigns second indices for identifying the motion vector predictors added in the second candidate list, and outputs the second indices and the motion vector difference; a prediction method decision unit that decisions 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 that codes prediction mode information indicating the inter prediction mode and the first index, or prediction mode information indicating the inter prediction mode, the second index, and the motion vector difference, wherein the first and second mode detection units use a plurality of common blocks as the plurality of reference blocks, wherein the first predetermined order for constructing the first candidate list in the first mode detection unit differs from the second predetermined order for constructing the second candidate list in the second mode detection unit, wherein the plurality of reference blocks include coded blocks spatially neighboring the block subject to coding and blocks included in a picture at a different point of time from a picture including the block subject to coding, wherein the first mode detection unit derives the coding information from the plurality of reference blocks such that a position of a block included in a picture at a different point of time in the first predetermined order is lower than a position of a spatially neighboring block in the first predetermined order, wherein the first mode detection unit constructs the first candidate list from a plurality of coded blocks spatially neighboring the block subject to coding in accordance with the first predetermined order, by providing a predetermined upper limit to the number of spatially neighboring coded blocks arranged in the first candidate list, and by using as many reference blocks as defined by the upper limit in the first predetermined order, and wherein a spatially neighboring left candidate block is at the top of the first predetermined order, followed by a candidate block above, a candidate block to the upper right, a candidate block to the lower left, a candidate block to the upper left, and a candidate block located in another picture at a different point of time.