Maximum Distance Separable Symbol-Pair Codes

We study (symbol-pair) codes for symbol- pair read channels introduced recently by Cassuto and Blaum (2010). A Singleton-type bound on symbol- pair codes is established and infinite families of optimal symbol- pair codes are constructed. These codes are maximum distance separable (MDS) in the sense that they meet the Singleton-type bound. In contrast to classical codes, where all known q-ary MDS codes have length O(q), we show that q-ary MDS symbol- pair codes can have length Omega(q(2)). We also construct equidistant cyclic MDS symbol- pair codes from Mendelsohn designs.