English

Wedge-Lifted Codes

Information Theory 2021-09-09 v2 math.IT

Abstract

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 tt-disjoint repair property (tt-DRGP). When t=N1/2dt = N^{1/2d}, where NN is the block length of the code and d2d \geq 2 is any integer, our codes give improved trade-offs between redundancy and locality among binary codes.

Keywords

Cite

@article{arxiv.2011.12435,
  title  = {Wedge-Lifted Codes},
  author = {Jabari Hastings and Amy Kanne and Ray Li and Mary Wootters},
  journal= {arXiv preprint arXiv:2011.12435},
  year   = {2021}
}

Comments

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 $\mathbb F_2$