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 -disjoint repair property (-DRGP). When , where is the block length of the code and 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 $\mathbb F_2$