Some Properties And Constructions Of Binary Optimal Locally Repairable Code

Recently,locally repairable codes(LRC)are widely used in storage systems,due to their functions to enhance the fault tolerance and the stability of the system,and binary LRCs with disjoint repair groups is a research hotspot.In 2017,Ge Gennian and others derived a new upper bound for the dimension of LRCs.Different from the C-M bound,new bound is only related to the code length,the locality and the minimum distance.This new upper bound is better than the C-M bound when the code length is large.In this thesis we give some examples of optimal codes with minimum distance (d=6 and(d=8.Similarly,we construct a code with minimum distance (d= 10 and then verify its optimality with respect to new bound.Moreover,a comparison by graph shows this new bound outperforms the C-M bound for given the code length,the locality and the minimum distance.