WebOptimal linear codes with a local-error-correction property. N. Prakash, G. Kamath, V. Lalitha, P. V. Kumar; ... This paper uses matrix-product codes to propose two infinite families of q-ary optimal (r, δ) locally repairable codes of lengths up to q + q and construction of a third family, which has unbounded lengths not divisible by r + δ − 1. Webgraph theoretically where it was shown that the scalar linear optimal solution is related to a rank minimization problem over a finite field. It turns out that (for a given field size), ...

On Optimal Locally Repairable Codes with Super-Linear Length

WebDec 31, 2024 · Locally repairable codes which are optimal with respect to the bound presented by Prakash et al. are considered. New upper bounds on the length of such optimal codes are derived. The new bounds both improve and generalize previously known bounds. Optimal codes are constructed, whose length is order-optimal when compared with the … WebSep 1, 2024 · In distributed storage systems, locally repairable codes (LRCs) can effectively reduce the complexity of repairing failed nodes. In this paper, we constructed six classes … fuk the rock 中古

Optimal cyclic locally repairable codes with unbounded length …

Webof optimal locally repairable codes with q =Θ(n) was pro-posed. In [33] and [37], optimal locally repairable codes were constructed using matroid theory.The constructionof [34] was generalized in [21] to include more flexible parameters when n q. Recently, in [23], cyclic optimal locally repairable codes with unbounded length were constructed ... WebDec 5, 2024 · Optimal LRC codes are those whose parameters achieve the generalized Singleton bound with equality. In the present paper, we are interested in studying optimal LRC codes over small fields and, more precisely, over $\mathbb{F}_4$. We shall adopt an approach by investigating optimal quaternary $(r,\delta)$-LRC codes through their parity … gilt terry cloth hoodie