On the MDS Condition of Blaum–Bruck–Vardy Codes With Large Number Parity Columns

Binary maximum distance separable (MDS) array codes are widely used in storage systems. EVENODD code and row-diagonal parity (RDP) code are two well-known binary MDS array codes with two parity columns. The Blaum-Bruck-Vardy (BBV) code is an extension of the double-erasure-correcting EVENODD code. It is known that the BBV code is always MDS for three parity columns, and sufficient conditions for up to eight parity columns to be MDS are also known. However, the MDS condition for more than eight parity columns is an open problem since then. In this letter, we study the MDS condition of BBV code and give a sufficient MDS condition of the BBV code with more than eight parity columns.