Maximum Distance Separable Codes for Symbol-Pair Read Channels
Yeow Meng Chee, Lijun Ji, Han Mao Kiah, Chengmin Wang, Jianxing Yin · IEEE Transactions on Information Theory · 2013
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 Ω(q2). In addition, we completely determine the existence of MDS symbol-pair codes for certain parameters.