Wedge-Lifted Codes

We define wedge-lifted codes, a variant of lifted codes, and we study their locality properties. We show that (taking the trace of) wedge-lifted codes yields binary codes with the
$t$
-disjoint repair property (
$t$
-DRGP). When
$t= N^{1/2d}$
, where
$N$
is the block length of the code and
$d\geq 2$
is any integer, our codes give improved trade-offs between redundancy and locality among binary codes.