Nilpotent Lie algebras having the Schur multiplier of maximum dimension

Let $L$ be an $n$-dimensional nilpotent Lie algebra of nilpotency class $c$ with the derived subalgebra of dimension $m$. Recently, Rai proved that the dimension of Schur multiplier of $L$ is bounded by $\frac{1}{2}(n-m-1)(n+m)-\sum\limits_{i=2}^ {min\lbrace n-m,c\rbrace} n-m-i$. In this paper, we obtain the structure of all nilpotent Lie algebras that attain this bound.