A new class of MDS symbol-pair codes

Abstract

The symbol-pair code is a new coding framework proposed to guard against pair-errors in symbol-pair read channels. Especially, a symbol-pair code with the parameters achieving the Singleton-type bound is called an MDS symbol-pair code. In this paper, inspiring by the classical construction for Reed-Solomon codes, for any $3\le k<m\le q-2$ and $m_1=\lfloor \frac{m}{\lfloor \frac{k-1}{2}\rfloor }\rfloor$, we construct a class of $q$-ary MDS symbol-pair codes with dimension $k$ and length $n$ $(n=m+m_1,m+m_1-1)$, where $q$ is a prime power. Furthermore, for $k\in \{3,4\}$, the symbol-pair weight distributions for these codes are determined by enumerating the number of polynomials with given roots.

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References in corpus (1)

• Linear Programming Decoding of Binary Linear Codes for Symbol-Pair Read Channels