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A primitive $k$-batch code encodes a string $x$ of length $n$ into string $y$of length $N$, such that each multiset of $k$ symbols from $x$ has $k$ mutuallydisjoint recovering sets from $y$. We develop new explicit and random codingconstructions of linear primitive batch codes based on finite geometry. In someparameter regimes, our proposed codes have lower redundancy than previouslyknown batch codes.

Constructions of Batch Codes via Finite Geometry