Abstract: Most of the existing locally repairable codes can meet the boundary condition of minimum distance, but it is difficult to construct the locally repairable codes with optimal dimension under the condition of minimum distance optimization. To solve this problems, this paper proposes a construction method of optimal locally repairable codes based on Hadamard matrix. By expanding Hadamard matrix, the check matrix of the optimal locally repairable code can be obtained. Specifically, the parity matrix of locally repairable codes is constructed using Hadamard matrix, and the minimum distance of the locally repairable codes constructed by the parity matrix can reach the optimal boundary, but its dimension does not reach the optimal dimension boundary condition. In order to improve the dimension, the element 0 and element 1 of the incidence matrix in the check matrix are exchanged to obtain a new incidence matrix. By cascading with the new incidence matrix, the constructed extended locally repairable code can not only achieve the minimum distance optimization, but also achieve the boundary condition of the optimal dimension. Compared with the existing locally repairable codes, the extended locally repairable code based on Hadamard matrix constructed in this paper is the optimal locally repairable code with minimum distance and dimension, and its code rate is closer to the boundary of the optimal code rate of locally repairable codes.