X-Code: MDS Array Codes with Optimal Encoding

Abstract

We present a new class of MDS array codes of size n x n (n a prime number) called X-Code. The X-Codes are of minimum column distance 3, namely, they can correct either one column error or two column erasures. The key novelty in X-code is that it has a simple geometrical construction which achieves encoding/update optimal complexity, namely, a change of any single information bit affects exactly two parity bits. The key idea in our constructions is that all parity symbols are placed in rows rather than columns.