Performance of transport protocols on lossy links is a well researched topic, however there are only a few proposals which make use of the opportunities presented by the use of erasure coding within the transport layer, particularly in the multipath transport protocol context. In this paper, we investigate the improvements in the performance of multipath SCTP transport protocol brought by the novel integration of the on-the-fly erasure code into the congestion control and reliability mechanisms of CMT-SCTP. Our contributions include: integration of transport protocol and erasure codes with regards to congestion control and reliability mechanisms; proposal for a variable retransmission delay parameter in the sender (aRTX) adjustment; evaluation of the performance of CMT-SCTP with erasure coding with simulations. Our results show that we can achieve from 10% to 80% improvements in application goodput under lossy multipath network conditions without a significant penalty i.e. with a minimal (10%) overhead due to the encoding-decoding process. We further evaluate the performance of video streaming using an equivalent of partially reliable CMT-SCTP with erasure coding and again demonstrate a solid performance improvement for our proposal, compared to CMT-SCTP. Finally, we provide an analytical evaluation of CMT-SCTP with erasure codes and validate this with simulation results.