When the base station apparatus determines that it is necessary to make the mobile station apparatus execute random access, it is determined whether there is an unused signature. Then, the validity period during which the mobile station apparatus can use a signature is determined and the end time of the validity period is calculated. The signature and the calculated end time are included into a random access preamble allocation message, which is transmitted to the mobile station apparatus. The mobile station apparatus extracts the signature and the end time from the random access preamble allocation message, and determines random access channels through which a random access preamble including the signature can be transmitted, based on the extracted end time. As a result, it is possible to provide a base station apparatus and the like which, even if the signature belongs to the validity period, can achieve efficient communication between the base station apparatus and the mobile station apparatus by assigning the signature to another mobile station apparatus.