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Journal articles on the topic 'Locally Recoverable Codes'

Author: Grafiati

Published: 6 September 2023

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1

Salgado, Cecilia, Anthony Varilly-Alvarado, and Jose Felipe Voloch. "Locally Recoverable Codes on Surfaces." IEEE Transactions on Information Theory 67, no. 9 (September 2021): 5765–77. http://dx.doi.org/10.1109/tit.2021.3090939.

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2

Kim, Boran. "Locally recoverable codes in Hermitian function fields with certain types of divisors." AIMS Mathematics 7, no. 6 (2022): 9656–67. http://dx.doi.org/10.3934/math.2022537.

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<abstract><p>A locally recoverable code with locality $ \bf r $ can recover the missing coordinate from at most $ {\bf r} $ symbols. The locally recoverable codes have attracted a lot of attention because they are more advanced coding techniques that are applied to distributed and cloud storage systems. In this work, we focus on locally recoverable codes in Hermitian function fields over $ \Bbb F_{q^2} $, where $ q $ is a prime power. With a certain type of divisor, we obtain an improved lower bound of the minimum distance for locally recoverable codes in Hermitian function fields. For doing this, we give explicit formulae of the dimension for some divisors of Hermitian function fields. We also present a standard that tells us when a divisor with certain places suggests an improved lower bound.</p></abstract>

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3

Barg, Alexander, Itzhak Tamo, and Serge Vladut. "Locally Recoverable Codes on Algebraic Curves." IEEE Transactions on Information Theory 63, no. 8 (August 2017): 4928–39. http://dx.doi.org/10.1109/tit.2017.2700859.

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4

Munuera, Carlos, and Wanderson Tenório. "Locally recoverable codes from rational maps." Finite Fields and Their Applications 54 (November 2018): 80–100. http://dx.doi.org/10.1016/j.ffa.2018.07.005.

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5

Galindo, Carlos, Fernando Hernando, and Carlos Munuera. "Locally recoverable J-affine variety codes." Finite Fields and Their Applications 64 (June 2020): 101661. http://dx.doi.org/10.1016/j.ffa.2020.101661.

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6

Tamo, Itzhak, and Alexander Barg. "A Family of Optimal Locally Recoverable Codes." IEEE Transactions on Information Theory 60, no. 8 (August 2014): 4661–76. http://dx.doi.org/10.1109/tit.2014.2321280.

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7

Ballico, E. "Locally Recoverable Codes correcting many erasures over small fields." Designs, Codes and Cryptography 89, no. 9 (July 6, 2021): 2157–62. http://dx.doi.org/10.1007/s10623-021-00905-4.

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AbstractWe define linear codes which are s-Locally Recoverable Codes (or s-LRC), i.e. codes which are LRC in s ways, the case $$s=1$$ s = 1 roughly corresponding to the classical case of LRC codes. We use them to describe codes which correct many erasures, although they have small minimum distance. Any letter of a received word may be corrected using s different local codes. We use the Segre embedding of s local codes and then a linear projection.

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8

Blaum, Mario, and Steven R. Hetzler. "Integrated interleaved codes as locally recoverable codes: properties and performance." International Journal of Information and Coding Theory 3, no. 4 (2016): 324. http://dx.doi.org/10.1504/ijicot.2016.079494.

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9

Cadambe, Viveck R., and Arya Mazumdar. "Bounds on the Size of Locally Recoverable Codes." IEEE Transactions on Information Theory 61, no. 11 (November 2015): 5787–94. http://dx.doi.org/10.1109/tit.2015.2477406.

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10

Tamo, Itzhak, Alexander Barg, and Alexey Frolov. "Bounds on the Parameters of Locally Recoverable Codes." IEEE Transactions on Information Theory 62, no. 6 (June 2016): 3070–83. http://dx.doi.org/10.1109/tit.2016.2518663.

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11

Agarwal, Abhishek, Alexander Barg, Sihuang Hu, Arya Mazumdar, and Itzhak Tamo. "Combinatorial Alphabet-Dependent Bounds for Locally Recoverable Codes." IEEE Transactions on Information Theory 64, no. 5 (May 2018): 3481–92. http://dx.doi.org/10.1109/tit.2018.2800042.

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12

Micheli, Giacomo. "Constructions of Locally Recoverable Codes Which are Optimal." IEEE Transactions on Information Theory 66, no. 1 (January 2020): 167–75. http://dx.doi.org/10.1109/tit.2019.2939464.

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13

Márquez-Corbella, Irene, Edgar Martínez-Moro, and Carlos Munuera. "Computing sharp recovery structures for locally recoverable codes." Designs, Codes and Cryptography 88, no. 8 (March 10, 2020): 1687–98. http://dx.doi.org/10.1007/s10623-020-00746-7.

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14

Li, Xiaoru, and Ziling Heng. "Constructions of near MDS codes which are optimal locally recoverable codes." Finite Fields and Their Applications 88 (June 2023): 102184. http://dx.doi.org/10.1016/j.ffa.2023.102184.

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15

Munuera, Carlos, Wanderson Tenório, and Fernando Torres. "Locally recoverable codes from algebraic curves with separated variables." Advances in Mathematics of Communications 14, no. 2 (2020): 265–78. http://dx.doi.org/10.3934/amc.2020019.

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16

Chen, Bocong, and Jing Huang. "A Construction of Optimal $(r,\delta)$ -Locally Recoverable Codes." IEEE Access 7 (2019): 180349–53. http://dx.doi.org/10.1109/access.2019.2957942.

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17

Rajput, Charul, and Maheshanand Bhaintwal. "RS-like locally recoverable codes with intersecting recovering sets." Finite Fields and Their Applications 68 (December 2020): 101729. http://dx.doi.org/10.1016/j.ffa.2020.101729.

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18

Liu, Jian, Sihem Mesnager, and Deng Tang. "Constructions of optimal locally recoverable codes via Dickson polynomials." Designs, Codes and Cryptography 88, no. 9 (February 15, 2020): 1759–80. http://dx.doi.org/10.1007/s10623-020-00731-0.

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19

Blaum, Mario. "Extended Integrated Interleaved Codes Over Any Field With Applications to Locally Recoverable Codes." IEEE Transactions on Information Theory 66, no. 2 (February 2020): 936–56. http://dx.doi.org/10.1109/tit.2019.2934134.

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20

López, Hiram H., Gretchen L. Matthews, and Ivan Soprunov. "Monomial-Cartesian codes and their duals, with applications to LCD codes, quantum codes, and locally recoverable codes." Designs, Codes and Cryptography 88, no. 8 (February 7, 2020): 1673–85. http://dx.doi.org/10.1007/s10623-020-00726-x.

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21

Zhang, Guanghui. "A New Construction of Optimal (r, δ) Locally Recoverable Codes." IEEE Communications Letters 24, no. 9 (September 2020): 1852–56. http://dx.doi.org/10.1109/lcomm.2020.2998587.

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22

Liu, Jian, Sihem Mesnager, and Lusheng Chen. "New Constructions of Optimal Locally Recoverable Codes via Good Polynomials." IEEE Transactions on Information Theory 64, no. 2 (February 2018): 889–99. http://dx.doi.org/10.1109/tit.2017.2713245.

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23

Kruglik, Stanislav, Kamilla Nazirkhanova, and Alexey Frolov. "New Bounds and Generalizations of Locally Recoverable Codes With Availability." IEEE Transactions on Information Theory 65, no. 7 (July 2019): 4156–66. http://dx.doi.org/10.1109/tit.2019.2897705.

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24

Ballico, Edoardo, and Chiara Marcolla. "Higher Hamming weights for locally recoverable codes on algebraic curves." Finite Fields and Their Applications 40 (July 2016): 61–72. http://dx.doi.org/10.1016/j.ffa.2016.03.004.

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25

Luo, Gaojun, and Xiwang Cao. "Constructions of Optimal Binary Locally Recoverable Codes via a General Construction of Linear Codes." IEEE Transactions on Communications 69, no. 8 (August 2021): 4987–97. http://dx.doi.org/10.1109/tcomm.2021.3083320.

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26

Qian, Jianfa, and Lina Zhang. "New Optimal Cyclic Locally Recoverable Codes of Length $n=2(q+1)$." IEEE Transactions on Information Theory 66, no. 1 (January 2020): 233–39. http://dx.doi.org/10.1109/tit.2019.2942304.

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27

Huang, Pengfei, Eitan Yaakobi, and Paul H. Siegel. "Multi-Erasure Locally Recoverable Codes Over Small Fields: A Tensor Product Approach." IEEE Transactions on Information Theory 66, no. 5 (May 2020): 2609–24. http://dx.doi.org/10.1109/tit.2019.2962012.

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28

Jin, Lingfei. "Explicit Construction of Optimal Locally Recoverable Codes of Distance 5 and 6 via Binary Constant Weight Codes." IEEE Transactions on Information Theory 65, no. 8 (August 2019): 4658–63. http://dx.doi.org/10.1109/tit.2019.2901492.

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29

Zhang, Xinmiao, and Zhenshan Xie. "Relaxing the Constraints on Locally Recoverable Erasure Codes by Finite Field Element Variation." IEEE Communications Letters 23, no. 10 (October 2019): 1680–83. http://dx.doi.org/10.1109/lcomm.2019.2927668.

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30

Su, Yi-Sheng. "Optimal Pliable Fractional Repetition Codes That are Locally Recoverable: A Bipartite Graph Approach." IEEE Transactions on Information Theory 65, no. 2 (February 2019): 985–99. http://dx.doi.org/10.1109/tit.2018.2876284.

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31

Bartoli, Daniele, Maria Montanucci, and Luciane Quoos. "Locally Recoverable Codes From Automorphism Group of Function Fields of Genus g ≥ 1." IEEE Transactions on Information Theory 66, no. 11 (November 2020): 6799–808. http://dx.doi.org/10.1109/tit.2020.2995852.

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32

Haymaker, Kathryn, Beth Malmskog, and Gretchen L. Matthews. "Locally recoverable codes with availability t≥2 from fiber products of curves." Advances in Mathematics of Communications 12, no. 2 (2018): 317–36. http://dx.doi.org/10.3934/amc.2018020.

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33

C., Pavan Kumar, and Selvakumar R. "Reliable and secure data communication in wireless sensor networks using optimal locally recoverable codes." Peer-to-Peer Networking and Applications 13, no. 3 (September 7, 2019): 742–51. http://dx.doi.org/10.1007/s12083-019-00809-0.

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34

Balaji, S. B., Ganesh R. Kini, and P. Vijay Kumar. "A Tight Rate Bound and Matching Construction for Locally Recoverable Codes With Sequential Recovery From Any Number of Multiple Erasures." IEEE Transactions on Information Theory 66, no. 2 (February 2020): 1023–52. http://dx.doi.org/10.1109/tit.2019.2958970.

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35

Gopalan, Parikshit, Cheng Huang, Bob Jenkins, and Sergey Yekhanin. "Explicit Maximally Recoverable Codes With Locality." IEEE Transactions on Information Theory 60, no. 9 (September 2014): 5245–56. http://dx.doi.org/10.1109/tit.2014.2332338.

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36

Mazumdar, Arya. "Capacity of Locally Recoverable Codes." IEEE Journal on Selected Areas in Information Theory, 2023, 1. http://dx.doi.org/10.1109/jsait.2023.3300901.

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37

Haymaker, Kathryn, and Justin O'Pella. "Locally recoverable codes from planar graphs." Journal of Algebra Combinatorics Discrete Structures and Applications, November 17, 2019, 33–51. http://dx.doi.org/10.13069/jacodesmath.645021.

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38

Li, Xiaoru, and Ziling Heng. "A construction of optimal locally recoverable codes." Cryptography and Communications, December 5, 2022. http://dx.doi.org/10.1007/s12095-022-00619-x.

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39

Blaum, Mario. "Multiple-Layer Integrated Interleaved Codes: A Class of Hierarchical Locally Recoverable Codes." IEEE Transactions on Information Theory, 2022, 1. http://dx.doi.org/10.1109/tit.2022.3166210.

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40

Li, Fagang, Hao Chen, Huimin Lao, and Shanxiang Lyu. "New upper bounds and constructions of multi-erasure locally recoverable codes." Cryptography and Communications, December 2, 2022. http://dx.doi.org/10.1007/s12095-022-00618-y.

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41

Xu, Li, Zhengchun Zhou, Jun Zhang, and Sihem Mesnager. "Optimal quaternary $$(r,\delta )$$-locally recoverable codes: their structures and complete classification." Designs, Codes and Cryptography, December 27, 2022. http://dx.doi.org/10.1007/s10623-022-01165-6.

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42

Xing, Chaoping, and Chen Yuan. "Construction of optimal (r, δ)-locally recoverable codes and connection with graph theory." IEEE Transactions on Information Theory, 2022, 1. http://dx.doi.org/10.1109/tit.2022.3157612.

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43

Dukes, Austin, Giacomo Micheli, and Vincenzo Pallozzi Lavorante. "Optimal locally recoverable codes with hierarchy from nested F-adic expansions." IEEE Transactions on Information Theory, 2023, 1. http://dx.doi.org/10.1109/tit.2023.3298401.

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44

Chara, María, Sam Kottler, Beth Malmskog, Bianca Thompson, and Mckenzie West. "Minimum distance and parameter ranges of locally recoverable codes with availability from fiber products of curves." Designs, Codes and Cryptography, March 4, 2023. http://dx.doi.org/10.1007/s10623-023-01189-6.

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45

Kazemi, Anahita, and Mehdi Ghiyasvand. "An upper bound on the minimum distance in locally recoverable codes with multiple localities and availability." Physical Communication, June 2023, 102124. http://dx.doi.org/10.1016/j.phycom.2023.102124.

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46

Krishnan, M. Nikhil. "Erasure Coding for Big Data." Advanced Computing and Communications, March 10, 2019. http://dx.doi.org/10.34048/2019.1.f1.

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This article deals with the reliable and efficient storage of ‘Big Data’, by which is meant the vast quantities of data that are stored in data centers worldwide. Given that storage units are prone to failure, to protect against data loss, data pertaining to a data file is stored in distributed and redundant fashion across multiple storage units. While replication was and continues to be commonly employed, the explosive growth in amount of data that is generated on a daily basis, has forced the industry to increasingly turn to erasure codes such as the Reed-Solomon code. The reason for this is that erasure codes have the potential to keep to a minimum, the storage overhead required to ensure a given level of reliability. There is also need for storing data such that the system can recover efficiently from the failure of a single storage unit. Conventional erasure-coding techniques are inefficient in this respect. To address this situation, coding theorists have come up with two new classes of erasure codes known respectively as regenerating codes and locally recoverable codes. These codes have served both to address the needs of industry as well as enrich coding theory by adding two new branches to the discipline. This article provides an overview of these exciting new developments, from the (somewhat biased) perspective of the authors.

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47

Doron, Dean, Dana Moshkovitz, Justin Oh, and David Zuckerman. "Nearly Optimal Pseudorandomness From Hardness." Journal of the ACM, August 10, 2022. http://dx.doi.org/10.1145/3555307.

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Existing proofs that deduce BPP = P from circuit lower bounds convert randomized algorithms into deterministic algorithms with a large polynomial slowdown. We convert randomized algorithms into deterministic ones with little slowdown . Specifically, assuming exponential lower bounds against randomized NP ∩ coNP circuits, formally known as randomized SVN circuits, we convert any randomized algorithm over inputs of length n running in time t ≥ n into a deterministic one running in time t 2 + α for an arbitrarily small constant α > 0. Such a slowdown is nearly optimal for t close to n , since under standard complexity-theoretic assumptions, there are problems with an inherent quadratic derandomization slowdown. We also convert any randomized algorithm that errs rarely into a deterministic algorithm having a similar running time (with pre-processing). The latter derandomization result holds under weaker assumptions, of exponential lower bounds against deterministic SVN circuits. Our results follow from a new, nearly optimal, explicit pseudorandom generator fooling circuits of size s with seed length (1 + α )log s , under the assumption that there exists a function f ∈ E that requires randomized SVN circuits of size at least \(2^{(1-\alpha ^{\prime })n} \) , where α = O ( α ′). The construction uses, among other ideas, a new connection between pseudoentropy generators and locally list recoverable codes.

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48

Shivakrishna, D., Aaditya M. Nair, and V. Lalitha. "Maximally Recoverable Codes with Hierarchical Locality: Constructions and Field-Size Bounds." IEEE Transactions on Information Theory, 2022, 1. http://dx.doi.org/10.1109/tit.2022.3212076.

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