Wedge-Lifted Codes

TL;DR

This paper introduces wedge-lifted codes, a new variant of lifted codes, demonstrating their improved redundancy-locality trade-offs and their binary versions with the $t$-disjoint repair property, relevant for efficient data repair.

Contribution

The paper defines wedge-lifted codes and analyzes their locality, showing how their trace yields binary codes with the $t$-disjoint repair property and improved trade-offs.

Findings

Wedge-lifted codes have favorable locality properties.

Binary codes with the $t$-disjoint repair property are obtained.

Trade-offs between redundancy and locality are improved for certain parameters.

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 $t$-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.