New constructions of MDS symbol-pair codes

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 large minimum pair-distance is interesting since such codes have the best possible error-correcting capability. A symbol-pair code attaining maximal minimum pair-distance is called a maximum distance separable (MDS) symbol-pair code. In this paper, we give a new construction of q-ary MDS symbol-pair codes with pair-distance 5 and length from 5 to q + q+1, which completely solves the case d = 5. For pair-distance 6 and length from 6 to q + 1, we construct MDS (n, 6)q symbol-pair codes by using a configuration called ovoid in projective geometry. With the help of elliptic curves, we present a construction of MDS symbol-pair codes for any pair-distance d and length d ≤ n ≤ q + ⌊2√q⌋ + δ(q)− 3, where δ(q) = 0 or 1. Index Terms Symbol-pair read channels, MDS symbol-pair codes, projective geometry, elliptic curves.