New Constructions of MDS Symbol-Pair Codes
Baokun Ding, Gennian Ge, Jun Zhang, Tao Zhang, Yiwei Zhang

TL;DR
This paper introduces new methods for constructing maximum distance separable (MDS) symbol-pair codes over finite fields, enhancing error correction in high-density data storage by leveraging geometric and algebraic structures.
Contribution
It provides explicit constructions of linear MDS symbol-pair codes with various pair-distances using projective geometry and elliptic curves, expanding the known parameters for such codes.
Findings
Existence of MDS symbol-pair codes with pair-distance 5 for lengths 5 to q^2+q+1.
Construction of MDS symbol-pair codes with pair-distance 6 using ovoids in projective geometry.
Development of codes with pair-distance d+2 for 7 ≤ d+2 ≤ n ≤ q + ⌊2√q⌋ + δ(q).
Abstract
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 . We show that a linear MDS symbol-pair code over with pair-distance exists if and only if the length ranges from to . As for codes with pair-distance , length ranging from to , we construct linear MDS symbol-pair codes by using a configuration…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsCoding theory and cryptography · Cooperative Communication and Network Coding · Cellular Automata and Applications
