Data stored in non-volatile memories may be destructed due to crosstalk and radiation but we can restore their data by using error-correcting codes. However, non-volatile memories consume a large amount of energy in writing. How to reduce maximum writing bits even using error-correcting codes is one of the challenges in non-volatile memory design. In this paper, we first propose Doughnut code which is based on state encoding limiting maximum and minimum Hamming distances. After that, we propose a code expansion method, which improves maximum and minimum Hamming distances. When we apply our code expansion method to Doughnut code, we can obtain a code which reduces maximum-flipped bits and has error-correcting ability equal to Hamming code. Experimental results show that the proposed code efficiently reduces the number of maximum-writing bits.