Genome memory is an important aspect of electronic cells. Here, a novel genome memory structure called partial-DNA cyclic memory is proposed, in which cells only store a portion of the system's entire DNA. The stored gene number is independent of the scale of embryonic array and of the target circuit, and can be set according to actual demand in the design process. Genes can be transferred in the cell and the embryonics array through intracellular and intercellular gene cyclic and non-cyclic shifts, and based on this process the embryonic array's functional differentiation and self-repair can be achieved. In particular, lost genes caused by faulty cells can be recovered through gene updating based on the remaining normal neighbor cells during the self-repair process. A reliability model of the proposed memory structure is built considering the gene updating method, and depending on the implementations of the memory, the hardware overhead is modeled. Based on the reliability model and hardware overhead model, we can find that the memory can achieve high reliability with relatively few gene backups and with low hardware overhead. Theoretical analysis and a simulation experiment show that the new genome memory structure not only achieves functional differentiation and self-repair of the embryonics array, but also ensures system reliability while reducing hardware overhead. This has significant value in engineering applications, allowing the proposed genome memory structure to be used to design larger scale self-repair chips.