An Improved MDS Condition of Blaum-Bruck-Vardy Codes

Abstract

Binary maximum distance separable (MDS) array codes play an important role in storage systems. The EVENODD code is a typical binary MDS array code with two parity columns and the Blaum-Bruck-Vardy (BBV) code with more parity columns is an extension of it. It has been shown that when the parameter p is large enough, the BBV code is always MDS. A sufficient MDS condition of the BBV code with more than eight parity columns was proposed before; however, the MDS condition is not tight. In this paper, we improve the MDS condition and present a tighter MDS condition.