2016/05/28 by Baokun Ding, Gennian Ge, Ding, Baokun +7 · 1 citation
Computer Science · Mathematics · #Cellular Automata and Applications #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1605.08859
openalex publication_date 2016/05/28 · arxiv created 2016/06/13 · arxiv updated 2016/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by the application of high-density data storage technologies, symbol-pair codes are proposed to protect against pair-errors in symbol-pair channels, whose outputs are overlapping pairs of symbols. The research of symbol-pair codes with the largest minimum pair-distance is interesting since such codes have the best possible error-correcting capability. A symbol-pair code attaining the maximal minimum pair-distance is called a maximum distance separable (MDS) symbol-pair code. In this paper, we focus on constructing linear MDS symbol-pair codes over the finite field \mathbbFq. We show that a linear MDS symbol-pair code over \mathbbFq with pair-distance 5 exists if and only if the length n ranges from 5 to q2+q+1. As for codes with pair-distance 6, length ranging from 6 to q2+1, we construct linear MDS symbol-pair codes by using a configuration called ovoid in projective geometry. With the help of elliptic curves, we present a construction of linear MDS symbol-pair codes for any pair-distance d+2 with length n satisfying 7≤ d+2≤ n≤ q+\lfloor 2√(q)\rfloor+δ(q)-3, where δ(q)=0 or 1.