An upper bound for B2[g] sets

Suppose g is a fixed positive integer. For N⩾2, a set A⊂Z∩[1,N] is called a B2[g] set if every integer n has at most g distinct representations as n=a+b with a,b∈A and a⩽b. In this paper, we give an upper bound estimate for the size of such A, improving the existing results.