3,444 research outputs found
Maximum Distance Separable Codes for Symbol-Pair Read Channels
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). In addition, we completely determine the
existence of MDS symbol-pair codes for certain parameters
New bounds for -Symbol Distances of Matrix Product Codes
Matrix product codes are generalizations of some well-known constructions of
codes, such as Reed-Muller codes, -construction, etc. Recently, a
bound for the symbol-pair distance of a matrix product code was given in
\cite{LEL}, and new families of MDS symbol-pair codes were constructed by using
this bound. In this paper, we generalize this bound to the -symbol distance
of a matrix product code and determine all minimum -symbol distances of
Reed-Muller codes. We also give a bound for the minimum -symbol distance of
codes obtained from the -construction, and use this bound to
construct some -linear -symbol almost MDS codes with arbitrary
length. All the minimum -symbol distances of -linear codes and
-linear codes for are determined. Some examples are
presented to illustrate these results
Several new classes of MDS symbol-pair codes derived from matrix-product codes
In order to correct the pair-errors generated during the transmission of
modern high-density data storage that the outputs of the channels consist of
overlapping pairs of symbols, a new coding scheme named symbol-pair code is
proposed. The error-correcting capability of the symbol-pair code is determined
by its minimum symbol-pair distance. For such codes, the larger the minimum
symbol-pair distance, the better. It is a challenging task to construct
symbol-pair codes with optimal parameters, especially,
maximum-distance-separable (MDS) symbol-pair codes. In this paper, the
permutation equivalence codes of matrix-product codes with underlying matrixes
of orders 3 and 4 are used to extend the minimum symbol-pair distance, and six
new classes of MDS symbol-pair codes are derived.Comment: 22 pages,1 tabl
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