Some Intersections of two Binary LRCs with Disjoint Repair Groups
2022 10th International Workshop on Signal Design and Its Applications in Communications (IWSDA)(2022)
摘要
In this paper, we investigate some properties of inter-sections of two binary
$(n, k, r)$
LRCs with disjoint repair groups when
$m\triangleq\frac{n}{r+1}$
is an integer. We first prove a necessary and sufficient condition for such an intersection to have availability 2. We prove as a corollary that such an intersection with availability 2 must be in fact a 3-seq LRC. Furthermore, we prove a bound on the dimension of such intersections and identify an interesting relation between this and the general rate bound on 3-seq LRCs.
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关键词
binary locally repairable codes,disjoint repair groups,availability,sequential-recovery LRCs
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