A method of transmitting information through an AWGN multiple access binary adder channel (BAC) will be addressed. We shall consider the following procedure of access to the channel: there are N users but only m, m < N, users are active (are transmitting their messages) during a fixed period of communication; the transmission is completely synchronized; the subset of the active users is known to the receiver. Such situation will be named transmission through BAC with a partial access (BACPA). If N ≫ m then time sharing is a very ineffective method for the BACPA. Indeed, since the subset of active users is unknown to each of the users, the time must be shared between all N users. Consequently, the overall transmission rate Rov is given by Rov = m/N R ≪ 1, where R is the coding rate of each user. We shall show that effective transmission through a BACPA can be realized by means of linear codes. More specifically, we shall show that for any noiseless BACPA it is possible to construct N linear codes such that Rov = 1 and the decoding error probability equals 0. For the case of AWGN BAC, we shall show that transmission by means of linear codes can have even better characteristics than time sharing.