1. A video image decoding device comprising: a variable length decoder that performs a variable-length decoding process on coded data multiplexed into a bitstream to obtain coding mode which indicates a prediction process performed to generate a prediction image, index information which specifies a motion vector for a coding block and control information for varying the number of motion vector candidates for each slice; and a motion compensator that performs a motion compensation prediction process on said coding block to generate a prediction image when said coding mode indicates inter prediction using a motion vector selected from one or more selectable motion vector candidates, said motion compensator selecting said motion vector from said motion vector candidates according to said index information; wherein said motion compensator prepares a list of said motion vector candidates including one or more spatial motion vectors which is obtained from a decoded block located around said coding block and/or a temporal motion vector which is obtained from a different picture which can be referred to by said coding block, said motion vector candidates being listed in accordance with a predetermined order, and said index information specifying a position in which one of said motion vector candidates exists within said list.
2. A video image decoding method comprising: performing a variable-length decoding process on coded data multiplexed into a bitstream to obtain coding mode which indicates a prediction process performed to generate a prediction image, index information which specifies a motion vector for a coding block and control information for varying the number of motion vector candidates for each slice; and performing a motion compensation prediction process on said coding block to generate a prediction image using a motion vector selected from one or more selectable motion vector candidates when said coding mode indicates inter prediction, said motion vector being selected from said motion vector candidates according to said index information; wherein said motion vector candidates include one or more spatial motion vectors which is obtained from a decoded block located around said coding block and/or a temporal motion vector which is

obtained from a decoded picture which can be referred to by said coding block, said motion vector candidates being listed in accordance with a predetermined order, and said index information specifying a position in which one of said motion vector candidates exists within said list.
3. A video image encoding device comprising: a motion compensator that performs a motion compensation prediction process on a coding block to generate a prediction image using a motion vector selected from one or more selectable motion vector candidates, said motion compensator selecting said motion vector from said motion vector candidates; a variable encoder that performs a variable-coding process to generate coding mode which indicates a prediction process performed to generate said prediction image, index information which specifies selected one of said motion vector candidates and control information for varying the number of said motion vector candidates for each slice; wherein said motion compensator prepares a list of said motion vector candidates including one or more spatial motion vectors which is obtained from a coded block located around said coding block and/or a temporal motion vector which is obtained from a different picture which can be referred to by said coding block, said motion vector candidates being listed in accordance with a predetermined order, and said index information specifying a position in which one of said motion vector candidates exists within said list.
4. A video image encoding method comprising: performing a motion compensation prediction process on a coding block to generate a prediction image using a motion vector selected from one or more selectable motion vector candidates, said motion compensator selecting said motion vector from said motion vector candidates; performing a variable-coding process to generate coding mode which indicates a prediction process performed to generate said prediction image, index information which specifies selected one of said motion vector candidates and control information for varying the number of said motion vector candidates for each slice; wherein said motion compensator prepares a list of said motion vector candidates including one or more spatial motion vectors which

is obtained from a coded block located around said coding block and/or a temporal motion vector which is obtained from a different picture which can be referred to by said coding block, said motion vector candidates being listed in accordance with a predetermined order, and said index information specifies a position in which one of said motion vector candidates exists within said list.
5. A video image decoding device comprising: a variable length decoder that performs a variable-length decoding process on coded data multiplexed into a bitstream to obtain compressed data, coding mode which indicates a prediction process performed to generate a prediction image, and index information which specifies a motion vector for a coding block, each associated with said coding block, and to obtain control information for varying the number of motion vector candidates for each slice, said coding block being obtained by hierarchically dividing an input image according to a maximum block size and an upper limit number of hierarchical layers; an intra predictor that performs an intra prediction process on said coding block to generate a prediction image when said coding mode indicates intra prediction; a motion compensator that performs a motion compensation prediction process on said coding block based on said coding mode to generate a prediction image when said coding mode indicates inter prediction, said motion compensator generating said prediction image using a motion vector selected from one or more selectable motion vector candidates according to said index information, said motion compensator selecting said motion vector indicated by said index information from said motion vector candidates; a decoded image generator that generates decoded image data by adding a difference image which is obtained by decoding said compressed data and said prediction image generated by said motion compensator; and a loop filter that performs filtering process on said decoded image data; wherein said motion compensator prepares a list of said motion vector candidates including one or more spatial motion vectors which is obtained from a decoded block located around said coding block and/or a temporal motion vector which is obtained from a decoded different picture which can be referred to by said coding block, said motion vector candidates being listed in accordance with a predetermined order, and said index

information specifying a position in which one of said motion vector candidates exists within said list, and said motion compensator selects said spatial motion vector or said temporal motion vector according to said index information.
6. A video image decoding method comprising: performing a variable-length decoding process on coded data multiplexed into a bitstream to obtain compressed data, coding mode which indicates a prediction process performed to generate a prediction image, index information which specifies a motion vector for a coding block, each associated with said coding block, and to obtain control information for varying the number of motion vector candidates for each slice, said coding block being obtained by hierarchically dividing an input image according to a maximum block size and an upper limit number of hierarchical layers; performing an intra prediction process on said coding block to generate a prediction image when said coding mode indicates intra prediction; performing a motion compensation prediction process on said coding block based on said coding mode to generate a prediction image when said coding mode indicates inter prediction, a motion compensator generating said prediction image using a motion vector selected from one or more selectable motion vector candidates, said motion vector being selected from said motion vector candidates according to said index information; generating decoded image data by adding a difference image which is obtained by decoding said compressed data and said prediction image; performing filtering process on said decoded image data; wherein said motion vector candidates include one or more spatial motion vectors which is obtained from a decoded block located around said coding block and/or a temporal motion vector which is obtained from a decoded picture which can be referred to by said coding block, said motion vector candidates being listed in accordance with a predetermined order, and said index information specifying a position in which one of said motion vector candidates exists within said list.