Locally repairable code (LRC) is a new family of erasure codes to reduce the repair bandwidth during recovering the lost data in distributed storage systems. Dependent on the characters of different distance and the parity check matrices of binary optimal codes, a method is presented to construct evendistance LRCs from odddistance LRCs, and some new LRCs with good properties are obtained by puncturing strategy. By using these two methods, four classes of LRCs (length n≤24, dimension k≥8 and distance 6≤d≤8)attained to the C-M bound are constructed. There is much in these methods of constructing LRCs that optimal LRCs with higher distance over binary field and general fields can be made use of.