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.

中文翻译：

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线性分解码和有限整数集覆盖

摘要 在本文中，我们研究了能够同时纠正多行擦除的并行纠删（PEC）矩阵码。我们的 PEC 码基于多项式的线性化分解 (LD)，我们表明 LD 码能够使用小的局部性集进行行擦除校正，即使大约有一半的行被擦除。我们还使用预定的邻域研究有限整数集的覆盖，并使用获得的覆盖估计来限制 LD 码的速率。