Abstract: Minimum storage regenerating codes have minimum storage of data in each node and therefore are maximal distance separable codes.Thus,the number of nodes is upper-bounded by 2b,where b is the bits of data stored in each node.From both theoretical and practical points of view,it is natural to consider regenerating codes that nearly have minimum storage of data,and meanwhile,the number of nodes is unbounded.Aiming at the problem,Jin et al.constructed the regenerating codes by algebraic geometry codes,which generalized the repairing algorithm of Reed-Solomon codes by Guruswami and Wotters.This paper mainly gives a construction to repair multiple failures for algebraic geometry codes,which extends the framework of repairing one failure for the regenerating codes. The results generalize some quite recent results in which regenerating codes,for instance,Reed-Solomon codes and scalar codes with multiple erasures.

Key words: distributed storage system, regenerating codes, Reed-Solomon codes, algebraic geometry codes, bandwidth