The $b$-weight distribution for MDS codes

For a positive integer $b\ge2$, the $b$-symbol code is a new coding framework proposed to combat $b$-errors in $b$-symbol read channels. Especially, a $2$-symbol code is called a symbol-pair code. Remarkably, a classical maximum distance separable (MDS) code is also an MDS $b$-symbol code. Recently, for any MDS code $\mathcal{C}$, Ma and Luo determined the symbol-pair weight distribution for $\mathcal{C}$. In this paper, by calculating the number of codewords in $\mathcal{C}$ with special shape, we obtain the $b$-weight distribution for $\mathcal{C}$, and then generalize Theorem $1$ in \cite{ML}.