Locally Recoverable Codes correcting many erasures over small fields

Abstract We define linear codes which are s -Locally Recoverable Codes (or -LRC), i.e. LRC in ways, the case $$s=1$$ s=1 roughly corresponding to classical of codes. use them describe correct many erasures, although they have small minimum distance. Any letter a received word may be corrected using different local Segre embedding and then projection.