Maximum Distance Separable Codes for Symbol-Pair Read Channels

摘要

We study (symbol-pair) codes for symbol-pair read channels introducedrecently by Cassuto and Blaum (2010). A Singleton-type bound on symbol-paircodes is established and infinite families of optimal symbol-pair codes areconstructed. These codes are maximum distance separable (MDS) in the sense thatthey meet the Singleton-type bound. In contrast to classical codes, where allknown q-ary MDS codes have length O(q), we show that q-ary MDS symbol-paircodes can have length \Omega(q^2). In addition, we completely determine theexistence of MDS symbol-pair codes for certain parameters.