Constructions of (r,t)-LRC Based on Totally Isotropic Subspaces in Symplectic Space Over Finite Fields

Abstract

Linear code with locality [Formula: see text] and availability [Formula: see text] is that the value at each coordinate [Formula: see text] can be recovered from [Formula: see text] disjoint repairable sets each containing at most [Formula: see text] other coordinates. This property is particularly useful for codes in distributed storage systems because it permits local repair of failed nodes and parallel access of hot data. In this paper, two constructions of [Formula: see text]-locally repairable linear codes based on totally isotropic subspaces in symplectic space [Formula: see text] over finite fields [Formula: see text] are presented. Meanwhile, comparisons are made among the [Formula: see text]-locally repairable codes we construct, the direct product code in Refs. [8], [11] and the codes in Ref. [9] about the information rate [Formula: see text] and relative distance [Formula: see text].