Title: Multi-Erasure Locally Recoverable Codes Over Small Fields For Flash Memory Array,
Abstract: Erasure codes play an important role in storage systems to prevent data loss.
In this work, we study a class of erasure codes called Multi-Erasure Locally
Recoverable Codes (ME-LRCs) for flash memory array. Compared to previous
related works, we focus on the construction of ME-LRCs over small fields. We
first develop upper and lower bounds on the minimum distance of ME-LRCs. These
bounds explicitly take the field size into account. Our main contribution is to
propose a general construction of ME-LRCs based on generalized tensor product
codes, and study their erasure-correcting property. A decoding algorithm
tailored for erasure recovery is given. We then prove that our construction
yields optimal ME-LRCs with a wide range of code parameters. Finally, we
present several families of ME-LRCs over different fields.