Recently, a novel BCS code differing from conventional concatenated (RS/BCH) codes has been proposed for LTE system. It achieved a significant improvement in the LTE system performance better than single codes and familiar concatenated (RS/BCH) codes. However, LTE systems that primarily depend on orthogonal frequency-division multiplexing (OFDM), no longer meet the demand of wireless-communication systems and their high data-rate requirements because of the rapid growth in the service aspect of such systems. In addition to high out-of-band emission (OOBE) and big peak to average power ratio (PAPR) of OFDM, it doesn’t meet the demand of 5G diverse service scenarios. Meanwhile, filtered OFDM (f-OFDM) is considered a candidate technique for 5G wireless communication systems which have OFDM features as well low OOBE. However, a trade-off exists among reducing OOBE, bit error rate (BER) degradation, and high PAPR. In this work, the BCS code is proposed for f-OFDM to enhance its system performance, while a root-raised-cosine windowed finite impulse response (FIR) filter is selected in f-OFDM to reduce OOBE levels. Results show that in the BPSK and QPSK modulation schemes, f-OFDM achieves a low level of OOBE after using an FIR digital filter against a high level of OFDM. Meanwhile, the proposed system using the BCS code enables remarkable improvement in BER performance and helps reduce PAPR better than conventional OFDM systems. Therefore, considering these features, the proposed system using the BCS code can be presented as a candidate for 5G wireless-communication systems.