Binary Locally Repairable Codes With Minimum Distance at Least Six Based on Partial $t$ -Spreads

Abstract

We propose a new construction for binary locally repairable codes (LRCs) based on a (partial) t-spread, which constructs an LRC with minimum distance d ≥ 6 and any locality r ≥ 2. Furthermore, we found that there are some cases in which the resulting codes are optimum in terms of the upper bound by Cadambe and Mazumdar in 2015.