On Distance Properties of $(r, t,x)$-LRC Codes
Stanislav Kruglik, Kamilla Nazirkhanova, Alexey Frolov · 2018
We continue our investigation of one possible generalization of locally recoverable codes (LRC) with all-symbol locality and availability when recovering sets can intersect in a small number of coordinates. This feature allows us to increase the achievable code rate and still meet load balancing requirements. In this paper we derive upper and lower bounds on the minimum distance of such codes. The upper bound is based on generalized Hamming weights (GHWs) that are fundamental parameters of any linear codes with many useful applications. In order to derive a lower bound we propose an explicit construction of (r, t, x), -LRC via rank-metric codes and previously developed high rate (r, t, x) -LRC codes.