We present two novel federated learning (FL) schemes that mitigate the effect of straggling devices by introducing redundancy on the devices' data across the network. Compared to other schemes in the literature, which deal with stragglers or device dropouts by ignoring their contribution, the proposed schemes do not suffer from the client drift problem. The first scheme, CodedPaddedFL, mitigates the effect of stragglers while retaining the privacy level of conventional FL. It combines one-time padding for user data privacy with gradient codes to yield straggler resiliency. The second scheme, CodedSecAgg, provides straggler resiliency and robustness against model inversion attacks and is based on Shamir's secret sharing. We apply CodedPaddedFL and CodedSecAgg to a classification problem. For a scenario with 120 devices, CodedPaddedFL achieves a speed-up factor of 18 for an accuracy of 95% on the MNIST dataset compared to conventional FL. Furthermore, it yields similar performance in terms of latency compared to a recently proposed scheme by Prakash et al. without the shortcoming of additional leakage of private data. CodedSecAgg outperforms the state-of-the-art secure aggregation scheme LightSecAgg by a speed-up factor of 6.6-18.7 for the MNIST dataset for an accuracy of 95%.