1. A decoding device for decoding a coded data of a digital image constituted by a plurality of blocks, comprising: a selecting circuit configured to select one or more adjacent blocks for a subject block, which is a subject for the decoding; a deriving circuit for deriving on the basis of a prediction mode(s) of the one or more adjacent blocks, an estimated prediction mode(s) to be estimated as an estimated value in intra-prediction mode estimation; a prediction mode decoding circuit for decoding, from the coded data, a prediction mode to be used in generation of a predicted image of the subject block, the prediction mode decoding circuit performing the decoding based on the estimated prediction mode(s) derived by the deriving circuit; and a predicted image generating circuit for generating a predicted image of the subject block, based on the prediction mode, the prediction mode decoding circuit decoding, for each of the plurality of blocks, a flag indicating whether or not an estimated prediction mode included in the group consisting of one or more estimated prediction modes for the block is identical with the prediction mode for the block, in a case where the flag is 1, the prediction mode decoding circuit designating the prediction mode of the subject block by (a) decoding an identifier mpm_idx and (b) referring to the identifier mpm_idx from among the one or more estimated prediction modes included in the group, and in a case where the flag is 0, the prediction mode decoding circuit designating the prediction mode of the subject block by (a′) decoding rem_bits and (b′) referring to the rem_bits from among prediction modes which are not included in the group.