Local recovery codes(LRC)are a class of linear codes. When the value of a component in the codeword is lost, it can be recovered by accessing a few (at most r) other components in the codeword. In this paper, we first construct LRC codes by using additive subgroups and multiplication subgroups as cosets on finite field F₂₇, and obtain that these LRC codes are optimal; Furthermore, we generalize to construct a cluster of optimal LRC codes for a general finite field F_3l with characteristic 3. Finally, the local resilience of these codes is compared with the latest LRC codes of the same kind. The results show that the constructed LRC codes have better local resilience.