Quantum telecommunication has received a lot of attention today by providing unconditional security because of the inherent nature of quantum channels based on the no-cloning theorem. In this mode of communication, first, the key is sent through a quantum channel that is resistant to eavesdropping, and then secure communication is established using the exchanged key. Due to the inevitability of noise, the received key needs to be distilled. One of the vital steps in key distillation is named key reconciliation which corrects the occurred errors in the key. Different solutions have been presented for this issue, with different efficiency and success rate. One of the most notable works is LDPC decoding which has higher efficiency compared to the others, but unfortunately, this method does not work well in the codes with a high rate. In this paper, we present an approach to correct the errors in the high rate LDPC code-based reconciliation algorithm. The proposed algorithm utilizes Integer Linear Programming to model the error correction problem to an optimization problem and solve it. Testing the proposed approach through simulation, we show it has high efficiency in high rate LDPC codes as well as a higher success rate compared with the LDPC decoding method -belief propagationin a reasonable time.