To reduce an operation amount (decoding time) more than that of an MLD decoding method when the number of transmission antennas is larger than that of reception antennas.

A decoder comprises: a generation part 30 for generating a plurality of candidate vectors on the basis of a reception signal vector; and a determination part 40 for determining a decoding signal vector from the plurality of candidate vectors by maximum likelihood detection. The generation part 30 decodes a transmission signal by assuming a value of another transmission signal to be any of values which the other transmission signal can take. The generation part 30 makes a set of the decoded transmission signal and a transmission signal whose value is assumed to be a candidate vector; and generates a plurality of candidate vectors from all sets of values that transmission signals, whose values is assumed, can take.