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.
Comment: 13 pages. Fixed a few typos found in Section 3.3 and Section 4 of the previous submission. The relevant bit patterns in Section 3.3 repeat mod $\ell'$ instead of mod $d$. The inner summation in Lemma 4.1 is over $\mathbb F_q$ and not $\mathbb F_2$