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Добірка наукової літератури з теми "Locally Recoverable Codes"

Автор: Grafiati
Опубліковано: 6 вересня 2023

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Статті в журналах з теми "Locally Recoverable Codes"

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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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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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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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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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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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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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Дисертації з теми "Locally Recoverable Codes"

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Balaji, S. B. "Erasure Codes for Distributed Storage: Tight Bounds and Matching Constructions." Thesis, 2018. https://etd.iisc.ac.in/handle/2005/5330.

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The reliable storage of Big Data across a spatially distributed network of nodes, calls for erasure-correcting codes that in addition to protecting against data loss, can also efficiently handle node repair. The need for node repair could arise on account of device failure, need for a maintenance reboot, or simply because the node is busy serving other demands. An important consideration here is the rate of the code, which is the ratio of the number of data symbols to the total amount of storage needed to reliably store these data symbols. In response, coding theorists have come up with two new classes of codes, known respectively as regenerating codes and Locally Recoverable Codes (LRC). While the focus of the thesis is on LRC, there are also contributions to the theory of regenerating codes. Contributions to LRC: A LRC is quite simply, a code where a given code symbol can be recovered by contacting at most r other code symbols, where the parameter r is much smaller than the dimension k of the code. A LRC with sequential recovery, is a code that can recover from an arbitrary set of trerasures in t steps in a sequential fashion. Each step recovers an erased symbol and makes use of at most r other code symbols comprising of unerased symbols as well as previously recovered symbols. In this thesis, a tight upper bound on the rate of LRC with sequential recovery is provided, for any value of the number t of erasures and any value of the locality parameter r ≥ 3. This bound proves an earlier conjecture due to Song, Cai and Yuen. While the bound is valid irrespective of the field over which the code is defined, a matching construction of binary codes that achieve the upper bound on rate is also presented. Contributions to Regenerating Codes: Regenerating codes aim to minimize the amount of data download needed to repair a failed node. Regenerating codes are linear codes that operate over a vector alphabet, i.e., each code symbol in a regenerating code is a vector of α symbols drawn from a field F. An important open question relates to the minimum possible value of α for a given storage overhead. Here we present tight lower bounds on α for the case when the codes belong to a certain class of codes called MSR codes as well as have the property of optimal access, i.e., symbols are accessed and transmitted as such without any computation by helper node for repair of a failed node. Contribution to availability Codes: A code in which each code symbol can be recovered in t different ways using respectively t pairwise disjoint set of code symbols with each set of size at most r is called a code with t-availability. The contributions of the thesis in the direction of t-availability codes include improved upper bounds on the minimum distance dmin of this class of codes, both with and without a constraint on the size q of the code-symbol alphabet. An improved upper bound on code rate R is also provided for a subclass of t-availability codes, termed as codes with strict availability. Among the class of t-availability codes, codes with strict availability typically have high rate. A complete characterization of optimal tradeoff between rate and fractional minimum distance for a special class of t-availability codes is also provided. There are additional results which are not mentioned above including results relating to a class of codes called maximum recoverable codes.
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Частини книг з теми "Locally Recoverable Codes"

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Barg, Alexander, Kathryn Haymaker, Everett W. Howe, Gretchen L. Matthews, and Anthony Várilly-Alvarado. "Locally Recoverable Codes from Algebraic Curves and Surfaces." In Association for Women in Mathematics Series, 95–127. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-63931-4_4.

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Mesnager, Sihem. "On Good Polynomials over Finite Fields for Optimal Locally Recoverable Codes." In Codes, Cryptology and Information Security, 257–68. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-16458-4_15.

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Heng, Ziling, and Xiaoru Li. "Near MDS Codes with Dimension 4 and Their Application in Locally Recoverable Codes." In Arithmetic of Finite Fields, 142–58. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-22944-2_8.

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Тези доповідей конференцій з теми "Locally Recoverable Codes"

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Mazumdar, Arya. "Capacity of Locally Recoverable Codes." In 2018 IEEE Information Theory Workshop (ITW). IEEE, 2018. http://dx.doi.org/10.1109/itw.2018.8613529.

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Barg, Alexander, Itzhak Tamo, and Serge Vladut. "Locally recoverable codes on algebraic curves." In 2015 IEEE International Symposium on Information Theory (ISIT). IEEE, 2015. http://dx.doi.org/10.1109/isit.2015.7282656.

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Tamo, Itzhak, and Alexander Barg. "A family of optimal locally recoverable codes." In 2014 IEEE International Symposium on Information Theory (ISIT). IEEE, 2014. http://dx.doi.org/10.1109/isit.2014.6874920.

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Bhadane, Sourbh, and Andrew Thangaraj. "Unequal locality and recovery for Locally Recoverable Codes with availability." In 2017 Twenty-third National Conference on Communications (NCC). IEEE, 2017. http://dx.doi.org/10.1109/ncc.2017.8077091.

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Senger, Christian, and Harsha Kadalveni Shivakumar. "Subfield Subcodes of Tamo–Barg Locally Recoverable Codes." In 2018 29th Biennial Symposium on Communications (BSC). IEEE, 2018. http://dx.doi.org/10.1109/bsc.2018.8494698.

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Huang, Pengfei, Eitan Yaakobi, and Paul H. Siegel. "Multi-erasure locally recoverable codes over small fields." In 2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton). IEEE, 2017. http://dx.doi.org/10.1109/allerton.2017.8262863.

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Ramkumar, Vinayak, Myna Vajha, and P. Vijay Kumar. "Locally Recoverable Streaming Codes for Packet-Erasure Recovery." In 2021 IEEE Information Theory Workshop (ITW). IEEE, 2021. http://dx.doi.org/10.1109/itw48936.2021.9611509.

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Tamo, Itzhak, and Alexander Barg. "Bounds on locally recoverable codes with multiple recovering sets." In 2014 IEEE International Symposium on Information Theory (ISIT). IEEE, 2014. http://dx.doi.org/10.1109/isit.2014.6874921.

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Cadambe, Viveck, and Arya Mazumdar. "An upper bound on the size of locally recoverable codes." In 2013 International Symposium on Network Coding (NetCod). IEEE, 2013. http://dx.doi.org/10.1109/netcod.2013.6570829.

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Garrison, Clifton, Giacomo Micheli, Logan Nott, Vincenzo Pallozzi Lavorante, and Phillip Waitkevich. "On a Class of Optimal Locally Recoverable Codes with Availability." In 2023 IEEE International Symposium on Information Theory (ISIT). IEEE, 2023. http://dx.doi.org/10.1109/isit54713.2023.10206840.

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