New asymptotic upper bounds are presented on the rate of sequences locally repairable codes (LRCs) with a prescribed relative minimum distance and locality over finite field $F$ . The apply to LRCs in which recovery functions linear; ...

In this work it is shown that locally repairable codes (LRCs) can be list-decoded efficiently beyond the Johnson radius for a large range of parameters by utilizing local error-correction capabilities. The corresponding decoding derived and asymptotic behavior analyzed. A general list-decoding algorithm LRCs achieves proposed along with an explicit realization are subcodes Reed-Solomon (such as...

We study the Singleton-type bound that provides an upper limit on minimum distance of locally repairable codes. present improved by carefully analyzing combinatorial structure repair sets. Thus, we show previous is unachievable for certain parameters. then also provide explicit constructions optimal codes which parameters new sharp. Additionally, as a byproduct, some previously known are shown ...

Abstract Mitral valve repair is a common and preferred technique over mitral replacement whenever it feasible. Transesophageal echocardiography (TEE) not only reliably identify repairable but also guide appropriate intervention. In addition to two-dimensional (2D) TEE, the three-dimensional (3D) clearly delineates size shape of apparatus, determine repairability success technique. We illustrate...

Solar energy is one of the immeasurable renewable in power generation for a green, clean and healthier environment. The silicon-layer solar panels absorb sun converts it into electricity by off-grid inverter. Electricity transferred either from this inverter or transformer, consumed consumption unit(s) available residential economic purposes. artificial neural network foundation intelligence so...

Two definitions of virtual age are considered. The first one is based on the fact that a system’s deterioration depends on an environment. In a more severe environment deterioration is more intensive and, therefore, the corresponding virtual age is larger than the calendar age. The second approach defines virtual age at the moment of switching from one regime to another. It is shown that both d...

In this paper, we provide fault-tolerant algorithms, for implementing atomic memory service in an asynchronous network of storage nodes, with the ability to perform background repair of crashed nodes, thereby increasing the durability of the storage service. A crashed node is assumed to lose all its data, both from the volatile memory as well as the stable storage. A repair operation of a node ...