Blockchain, a specific distributed database which maintains a list of data records against tampering and corruption, has aroused wide interests and become a hot topic in the real world. Nevertheless, the increasingly heavy storage consumption brought by the full-replication data storage mechanism, becomes a bottleneck to the system scalability. To address this problem, a reliable storage scheme named BFT-Store (Qiet al.2020), integrating erasure coding with Byzantine Fault Tolerance (BFT), was proposed recently. While, three critical problems are still left open: (i) The complex re-initialization process of the blockchain when the number of nodes varies; (ii) The high computational overload of downloading data; (iii) The massive communication on the network. This paper proposes a better trade-off for blockchain storage scheme termed PartitionChain which addresses the above three problems, maintaining the merits of BFT-Store. First, our scheme allows the original nodes to merely update a single aggregate signature (e.g., 320 bits) when the number of nodes varies. Using aggregate signatures as the proof of the encoded data not only saves the storage costs but also gets rid of the trusted third party. Second, the computational complexity of retrieving data by decoding, compared to BFT-Store, is greatly reduced by about$2^{18}$times on each node. Third, the amount of transmitted data for recovering each block is reduced from$O(n)$(assuming$n$is the number of nodes) to$O(1)$, by partitioning each block into smaller pieces and applying Reed-Solomon coding to each block. Furthermore, this paper also introduces a reputation ranking system where the malicious behaviors of the nodes can be detected and marked, enabling PartitionChain to check the credits of each node termly and expel the nodes with misbehavior to the specific extent. Comparing with BFT-Store, our scheme allows blockchain system to suit dynamic network with higher efficiency and scalability.