Abstract
In this paper, we study parallel erasure correction (PEC) matrix codes capable of correcting multiple row erasures simultaneously. Our PEC codes are based on linearized decomposition (LD) of polynomials and we show that the LD codes are capable of row erasure correction using small locality sets, even if roughly half the rows are erased. We also study coverings of finite set of integers using predetermined neighbourhoods and use the covering estimate obtained, to bound the rate of LD codes.
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