20 papers · ranked by Valyu relevance
Anina Gruica, Benjamin Jany, Alberto Ravagnani
We develop a duality theory of locally recoverable codes (LRCs) and apply it to establish a series of new bounds on their parameters. We introduce and study a refined notion of weight distribution that captures the code’s locality. Using a duality result analogous to a MacWilliams identity, we then derive an LP-type…
Carlos Munuera
A locally recoverable code is an error-correcting code such that any erasure in a coordinate of a codeword can be recovered from a set of other few coordinates. In this article we introduce a model of local recoverable codes that also includes local error detection. The cases of the Reed-Solomon and Locally Recoverable…
Arya Mazumdar
Motivated by applications in distributed storage, the notion of a locally recoverable code (LRC) was introduced a few years back. In an LRC, any coordinate of a codeword is recoverable by accessing only a small number of other coordinates. While different properties of LRCs have been well-studied, their performance on…
Yu Zhang, Xiangqiong Zeng, Eirik Rosnes, Yauhen Yakimenka
In this paper, we generalize the construction of locally repairable codes (LRCs) by leveraging pairwise balanced designs (PBDs) and balanced incomplete block designs (BIBDs) to construct codes with nonuniform locality or nonuniform availability. Our constructions prioritize binary implementations for practical…
Kathryn Haymaker, Beth Malmskog, Gretchen L. Matthews
Codes with locality, also known as locally recoverable codes, allow for recovery of erasures using proper subsets of other coordinates. Theses subsets are typically of small cardinality to promote recovery using limited network traffic and other resources. Hierarchical locally recoverable codes allow for recovery of…
Brett Hemenway, Noga Ron‐Zewi, Mary Wootters
In this work, we give the first construction of high-rate locally list-recoverable codes. Listrecovery has been an extremely useful building block in coding theory, and our motivation is to use these codes as such a building block. In particular, our construction gives the first capacity-achieving locally…
Daniel Augot, Françoise Levy-dit-Vehel, Abdullatif Shikfa
Since the concept of locally decodable codes was introduced by Katz and Trevisan in 2000 [11], it is well-known that information theoretically secure private information retrieval schemes can be built using locally decodable codes [15]. In this paper, we construct a Byzantine robust PIR scheme using the multiplicity…
Kang-Seok Lee, Hosung Park, Jong-Seon No
In this paper, a new family of binary LRCs (BLRCs) with locality 2 and uneven availabilities for hot data is proposed, which has a high information symbol availability and low parity symbol availabilities for the local repair of distributed storage systems. The local repair of each information symbol for the proposed…
M. Nikhil Krishnan, Bhagyashree Puranik, P. Vijay Kumar, Itzhak Tamo + 1 more
'Alexander Barg'] In this paper, we study the impact of locality on the decoding of binary cyclic codes under two approaches, namely ordered statistics decoding (OSD) and trellis decoding. Given a binary cyclic code having locality or availability, we suitably modify the OSD to obtain gains in terms of the…
Licheng Mao, Shenghao Yang, Xuan Huang, Yanyan Dong + 1 more
Systematic codes are of important practical interest for communications. Network coding, however, seems to conflict with systematic codes: although the source node can transmit message packets, network coding at the intermediate network nodes may significantly reduce the number of message packets received by the…
Wien Hong, Xiaoyu Zhou, Der-Chyuan Lou, He Debiao
In this paper, we propose an efficient method for authenticating the absolute moment block truncation coding (AMBTC) compressed images with the capability to recover tampered blocks. The existing methods may not be able to detect some types of intentional tampering. Meanwhile, the tampered blocks are only recovered by…
Jingcheng Zhang, Lei Chen, Jinlin Sun, Shumin Li + 5 more
DNA has emerged as a compelling archival storage medium, offering unprecedented information density and millennia-scale durability. Despite its promise, DNA-based data storage faces critical challenges due to error-prone processes during DNA synthesis, storage, and sequencing. In this study, we introduce Gungnir, a…
Ian Holmes
We describe a strategy for constructing codes for DNA-based information storage by serial composition of weighted finite-state transducers. The resulting state machines can integrate correction of substitution errors; synchronization by interleaving watermark and periodic marker signals; conversion from binary to…
Shubham Chandak, Joachim Neu, Kedar Tatwawadi, Jay Mardia + 7 more
As magnetization and semiconductor based storage technologies approach their limits, bio-molecules, such as DNA, have been identified as promising media for future storage systems, due to their high storage density (petabytes/gram) and long-term durability (thousands of years). Furthermore, nanopore DNA sequencing…
Julie D. Thompson, Raymond Ripp, Claudine Mayer, Olivier Poch + 1 more
The X circular code is a set of 20 trinucleotides (codons) that has been identified in the protein-coding genes of most organisms (bacteria, archaea, eukaryotes, plasmids, viruses). It has been shown previously that the X circular code has the important mathematical property of being an error-correcting code. Thus…
Lifu Song, Feng Geng, Ziyi Gong, Bingzhi Li + 1 more
High density and long-term features make DNA data storage a potential media. However, DNA data channel is a unique channel with unavoidable ‘data reputations’ in the forms of multiple error-rich strand copies. This multi-copy feature cannot be well harnessed by available codec systems optimized for single-copy media.…
Authors not listed
Machine learning models are increasingly applied to heterogeneous materials datasets spanning different synthesis routes, measurement protocols, and structural classes. Although multi-task and representation-learning approaches are commonly used to improve predictive performance, the latent representations learned by…
Eugenio Marinelli, Yiqing Yan, Virginie Magnone, Marie-Charlotte Dumargne + 3 more
The surge in demand for cost-effective, durable long-term archival media, coupled with density limitations of contemporary magnetic media, has resulted in synthetic DNA emerging as a promising new alternative. Today, the limiting factor for DNA-based data archival is the cost of writing (synthesis) and reading…
Authors not listed
This work provides a rigorous theoretical investigation of selective error correction strategies for variational quantum algorithms, with focus on understanding the interplay between error suppression, circuit trainability, and computational resource requirements. We develop a mathematical framework that characterizes…
Authors not listed
The Hidden Subgroup Problem (HSP) unifies several landmark quantum algorithms, yet systematic exploration of its variants and modern applications has slowed. This paper revives HSP-based algorithm design by examining new group structures with direct relevance to post-quantum cryptography, lattice problems, and…