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X-code: MDS array codes with optimal encoding

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2 Author(s)
Lihao Xu ; California Inst. of Technol., Pasadena, CA, USA ; Bruck, J.

We present a new class of MDS (maximum distance separable) array codes of size n×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, i.e., 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

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Information Theory, IEEE Transactions on  (Volume:45 ,  Issue: 1 )