  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 $k$ mutually
disjoint recovering sets from $y$. We develop new explicit and random coding
constructions of linear primitive batch codes based on finite geometry. In some
parameter regimes, our proposed codes have lower redundancy than previously
known batch codes.
