Related papers: Optimal Quantum $(r,δ)$-Locally Repairable Codes via Classical Ones

Optimal Quantum $(r,δ)$-Locally Repairable Codes via Classical Ones

URL: http://arxiv.org/abs/2507.18175v1
Date: Thu, 24 Jul 2025 08:21:20 GMT
Title: Optimal Quantum $(r,δ)$-Locally Repairable Codes via Classical Ones
Authors: Kun Zhou, Meng Cao,
Abstract summary: Local repairable codes (LRCs) play a crucial role in mitigating data loss in large-scale distributed and cloud storage systems.<n>This paper establishes a unified decomposition theorem for general optimal $(r,delta)$-LRCs.<n>We construct three infinite families of optimal quantum $(r,delta)$-LRCs with flexible parameters.
Score: 52.3857155901121
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: Locally repairable codes (LRCs) play a crucial role in mitigating data loss in large-scale distributed and cloud storage systems. This paper establishes a unified decomposition theorem for general optimal $(r,\delta)$-LRCs. Based on this, we obtain that the local protection codes of general optimal $(r,\delta)$-LRCs are MDS codes with the same minimum Hamming distance $\delta$. We prove that for general optimal $(r,\delta)$-LRCs, their minimum Hamming distance $d$ always satisfies $d\geq \delta$. We fully characterize the optimal quantum $(r,\delta)$-LRCs induced by classical optimal $(r,\delta)$-LRCs that admit a minimal decomposition. We construct three infinite families of optimal quantum $(r,\delta)$-LRCs with flexible parameters.

Related papers

Optimal Quantum $(r,δ)$-Locally Repairable Codes From Matrix-Product Codes [52.3857155901121]
We study optimal quantum $(r,delta)$-LRCs from matrix-product (MP) codes.<n>We present five infinite families of optimal quantum $(r,delta)$-LRCs with flexible parameters.
arXiv Detail & Related papers (2025-08-05T16:05:14Z)
Quantum $(r,δ)$-locally recoverable codes [41.08639347877682]
A classical $(r,delta)$-locally recoverable code is an error-correcting code such that, for each coordinate $c_i$ of a codeword, there exists a set of at most $r+ delta -1$ coordinates containing $c_i$.<n>These codes are useful for avoiding loss of information in large scale distributed and cloud storage systems.
arXiv Detail & Related papers (2024-12-21T11:45:32Z)
Learning Networks from Wide-Sense Stationary Stochastic Processes [7.59499154221528]
A key inference problem here is to learn edge connectivity from node outputs (potentials)<n>We use a Whittle's maximum likelihood estimator (MLE) to learn the support of $Last$ from temporally correlated samples.<n>We show that the MLE problem is strictly convex, admitting a unique solution.
arXiv Detail & Related papers (2024-12-04T23:14:00Z)
Transfer Q Star: Principled Decoding for LLM Alignment [105.89114186982972]
Transfer $Q*$ estimates the optimal value function for a target reward $r$ through a baseline model. Our approach significantly reduces the sub-optimality gap observed in prior SoTA methods.
arXiv Detail & Related papers (2024-05-30T21:36:12Z)
Mind the gap: Achieving a super-Grover quantum speedup by jumping to the end [114.3957763744719]
We present a quantum algorithm that has rigorous runtime guarantees for several families of binary optimization problems. We show that the algorithm finds the optimal solution in time $O*(2(0.5-c)n)$ for an $n$-independent constant $c$. We also show that for a large fraction of random instances from the $k$-spin model and for any fully satisfiable or slightly frustrated $k$-CSP formula, statement (a) is the case.
arXiv Detail & Related papers (2022-12-03T02:45:23Z)
Best Policy Identification in Linear MDPs [70.57916977441262]
We investigate the problem of best identification in discounted linear Markov+Delta Decision in the fixed confidence setting under a generative model. The lower bound as the solution of an intricate non- optimization program can be used as the starting point to devise such algorithms.
arXiv Detail & Related papers (2022-08-11T04:12:50Z)
Nearly Optimal Policy Optimization with Stable at Any Time Guarantee [53.155554415415445]
Policy-based method in citetshani 2020optimistic is only $tildeO(sqrtSAH3K + sqrtAH4K)$ where $S$ is the number of states, $A$ is the number of actions, $H$ is the horizon, and $K$ is the number of episodes, and there is a $sqrtSH$ gap compared with the information theoretic lower bound $tildeOmega(sqrtSAH
arXiv Detail & Related papers (2021-12-21T01:54:17Z)
Agnostic Reinforcement Learning with Low-Rank MDPs and Rich Observations [79.66404989555566]
We consider the more realistic setting of agnostic RL with rich observation spaces and a fixed class of policies $Pi$ that may not contain any near-optimal policy. We provide an algorithm for this setting whose error is bounded in terms of the rank $d$ of the underlying MDP.
arXiv Detail & Related papers (2021-06-22T03:20:40Z)
On Efficient Low Distortion Ultrametric Embedding [18.227854382422112]
A widely-used method to preserve the underlying hierarchical structure of the data is to find an embedding of the data into a tree or an ultrametric. In this paper, we provide a new algorithm which takes as input a set of points isometric in $mathbbRd2 (for universal constant $rho>1$) to output an ultrametric $Delta. We show that the output of our algorithm is comparable to the output of the linkage algorithms while achieving a much faster running time.
arXiv Detail & Related papers (2020-08-15T11:06:45Z)

This list is automatically generated from the titles and abstracts of the papers in this site.