List Decodability of Symbol-Pair Codes

Abstract

We investigate the list decodability of symbol-pair codes in the present paper. Firstly, we show that list decodability of every symbol-pair code does not exceed the Gilbert-Varshamov bound. On the other hand, we are able to prove that with high probability, a random symbol-pair code can be list decoded up to the Gilbert-Varshamov bound. Our second result of this paper is to derive the Johnson-type bound, i.e., a lower bound on list decoding radius in terms of minimum distance. Finally, we present a list decoding algorithm of Reed-Solomon codes beyond the Johnson-type bound. * Shu Liu was with the National

Constructions of MDS symbol-pair codes with minimum distance seven or eight

“…Recently, some new results on constructing symbolpair codes were presented in [12,14]. Moreover, some decoding algorithms of symbol-pair codes were proposed by various researchers in [15,21,24,26,27] and the symbol-pair weight distributions of some linear codes over finite fields were studied in [10,11,13,25] and the references therein.…”

A new class of MDS symbol-pair codes

“…In 2012, Yaakobi et al [25] proposed an efficient decoding algorithm for cyclic symbol-pair codes. Later, there are further reasearch for symbol-pair codes including constructions for symbol-pair codes [3-7, 10, 12, 15-17, 20, 21], some decoding algorithms for symbolpair codes [13,18,[23][24][25], and symbol-pair weight distributions for some linear codes [8,9,11,22,26], and so on.…”

Generalized Pair Weights of Linear Codes and Linear Isomorphisms Preserving Pair Weights

“…Chen, Lin and Liu [3] presented three lower bounds for the minimum pair distance of constacyclic codes and obtained new MDS symbol-pair codes with minimum pair distance seven and eight through repeated-root cyclic codes. In [9], Liu, Xing and Yuan presented the list decodability of symbol-pair codes and a list decoding algorithm of Reed-Solomon codes beyond the Johnson-type bound in the pair weight. In [5] and [4], the authors calculated the symbol-pair distances of repeated-root constacyclic codes of lengths p s and 2p s , respectively.…”