Maximum Distance Separable Codes for Symbol-Pair Read Channels

Abstract—We study (symbol-pair) codes for symbol-pair read channels introduced recently by Cassuto and Blaum (2010). A Sin-gleton-type bound on symbol-pair codes is established and infinite families of optimal symbol-pair codes are constructed. These codes aremaximumdistance separable (MDS) in the sense that theymeet the Singleton-type bound. In contrast to classical codes, where all known-ary MDS codes have length, we show that-ary MDS symbol-pair codes can have length. In addition, we completely determine the existence of MDS symbol-pair codes for certain parameters. Index Terms—Codes for magnetic storage, maximal distance separable, Singleton-type bound, symbol-pair read channels. I