Have a personal or library account? Click to login
Fractal codes with locality and availability Cover
Open Access
|Aug 2025

References

  1. W. Jiang, H. Jiang, J. Wu and Q. Chen, “Accelerating Distributed Cloud Storage Systems with In-Network Computing,” in IEEE Network, vol. 37, no. 4, pp. 64-70, July/August 2023, doi: 10.1109/MNET.002.2200631.
  2. S. Rafati Niya; B. Stiller, “Enabling Technologies and Distributed Storage,” in Blockchains: Empowering Technologies and Industrial Applications, IEEE, 2024, pp. 21-51, doi: 10.1002/9781119781042.ch2.
  3. A. G. Dimakis, K. Ramchandran, Y. Wu and C. Suh, “A Survey on Network Codes for Distributed Storage,” in Proceedings of the IEEE, vol. 99, no. 3, pp. 476-489, March 2011, doi: 10.1109/JPROC.2010.2096170.
  4. M. Blaum, J. Brady, J. Bruck and Jai Menon, “EVENODD: an efficient scheme for tolerating double disk failures in RAID architectures,” in IEEE Transactions on Computers, vol. 44, no. 2, pp. 192-202, Feb. 1995, doi: 10.1109/12.364531.
  5. B. H. Marcus, R. M. Roth, and P. H. Siegel, “Constrained systems and coding for recording channels,” in Handbook of Coding Theory, V. Pless and W. C. Huffman, Eds., 1998, pp. 1635–1764
  6. P. Gopalan, C. Huang, H. Simitci and S. Yekhanin, “On the Locality of Codeword Symbols,” in IEEE Transactions on Information Theory, vol. 58, no. 11, pp. 6925-6934, Nov. 2012, doi: 10.1109/TIT.2012.2208937.
  7. M. Shahabinejad, M. Khabbazian and M. Ardakani, “A Class of Binary Locally Repairable Codes,” in IEEE Transactions on Communications, vol. 64, no. 8, pp. 3182-3193, Aug. 2016, doi: 10.1109/TCOMM.2016.2581163.
  8. B. Zhu and H. Li, “Exploring Node Repair Locality in Fractional Repetition Codes,” in IEEE Communications Letters, vol. 20, no. 12, pp. 2350-2353, Dec. 2016, doi: 10.1109/LCOMM.2016.2605100.
  9. X. Zhang, “Modified Generalized Integrated Interleaved Codes for Local Erasure Recovery,” in IEEE Communications Letters, vol. 21, no. 6, pp. 1241-1244, June 2017, doi: 10.1109/LCOMM.2017.2675905.
  10. X. Zhang, S. Sprouse and I. Ilani, “A Flexible and Low-Complexity Local Erasure Recovery Scheme,” in IEEE Communications Letters, vol. 20, no. 11, pp. 2129-2132, Nov. 2016, doi: 10.1109/LCOMM.2016.2604307.
  11. M.-Y. Nam and H. -Y. Song, “Binary Locally Repairable Codes with Minimum Distance at Least Six Based on Partial t -Spreads,” in IEEE Communications Letters, vol. 21, no. 8, pp. 1683-1686, Aug. 2017, doi: 10.1109/LCOMM.2017.2697424.
  12. M. Shahabinejad, M. Khabbazian and M. Ardakani, “On the Average Locality of Locally Repairable Codes,” in IEEE Transactions on Communications, vol. 66, no. 7, pp. 2773-2783, July 2018, doi: 10.1109/TCOMM.2017.2712186.
  13. X. Zhang and Z. Xie, “Relaxing the Constraints on Locally Recoverable Erasure Codes by Finite Field Element Variation,” in IEEE Communications Letters, vol. 23, no. 10, pp. 1680-1683, Oct. 2019, doi: 10.1109/LCOMM.2019.2927668.
  14. C. Rajput and M. Bhaintwal, “Cyclic LRC-LCD Codes with Hierarchical Locality,” in IEEE Communications Letters, vol. 25, no. 3, pp. 711-715, March 2021, doi: 10.1109/LCOMM.2020.3040170.
  15. Q. Fu, R. Li and S. Yang, “Optimal (r, δ)-Locally Repairable Codes from Simplex Code and Cap Code,” in IEEE Access, vol. 8, pp. 215414-215418, 2020, doi: 10.1109/ACCESS.2020.3040320.
  16. B. Andrade, C. Carvalho, V. G. L. Neumann and A. C. P. Veiga, “A Family of Codes with Locality Containing Optimal Codes,” in IEEE Access, vol. 10, pp. 39145-39153, 2022, doi: 10.1109/ACCESS.2022.3165032.
  17. X. Lin, “A Note on Bandwidth-Optimal Repair Scheme for Reed-Solomon Codes with Low Repair Locality,” in IEEE Communications Letters, vol. 27, no. 11, pp. 2924-2927, Nov. 2023, doi: 10.1109/LCOMM.2023.3319653.
  18. J. Wang, K. Shen, X. Liu and C. Yu, “Construction of Binary Locally Repairable Codes with Optimal Distance and Code Rate,” in IEEE Communications Letters, vol. 25, no. 7, pp. 2109-2113, July 2021, doi: 10.1109/LCOMM.2021.3075520.
  19. A. Singh Rawat, D. S. Papailiopoulos and A. G. Dimakis, “Availability and locality in distributed storage,” 2013 IEEE Global Conference on Signal and Information Processing, Austin, TX, USA, 2013, pp. 923-928, doi: 10.1109/GlobalSIP.2013.6737043.
  20. J. Hao and S.-T. Xia, “Constructions of Optimal Binary Locally Repairable Codes with Multiple Repair Groups,” in IEEE Communications Letters, vol. 20, no. 6, pp. 1060-1063, June 2016, doi: 10.1109/LCOMM.2016.2539160.
  21. J.-H. Kim and H.-Y. Song, “Alphabet-Dependent Bounds for Locally Repairable Codes with Joint Information Availability,” in IEEE Communications Letters, vol. 21, no. 8, pp. 1687-1690, Aug. 2017, doi: 10.1109/LCOMM.2017.2699968.
  22. N. Silberstein, A. Zeh, “Anticode-based locally repairable codes with high availability,” Designs, Codes and Cryptography, pp. 419-445, 2018, doi: 86. 10.1007/s10623-017-0358-0.
  23. C. Kim and J.-S. No, “New Constructions of Binary LRCs with Disjoint Repair Groups and Locality 3 Using Existing LRCs,” in IEEE Communications Letters, vol. 23, no. 3, pp. 406-409, March 2019, doi: 10.1109/LCOMM.2019.2892950.
  24. U. D. Kadiyam and S. Das, “A Class of Codes with Availability and Multiple Local-Erasures Correction,” in IEEE Communications Letters, vol. 24, no. 10, pp. 2087-2091, Oct. 2020, doi: 10.1109/LCOMM.2020.3004757.
  25. G. Zhang, “A New Construction of Optimal (r, δ) Locally Recoverable Codes,” in IEEE Communications Letters, vol. 24, no. 9, pp. 1852-1856, Sept. 2020, doi: 10.1109/LCOMM.2020.2998587.
  26. U. D. Kadiyam and S. Das, “Codes with Availability for Multiple Code Symbols,” in IEEE Communications Letters, vol. 25, no. 8, pp. 2477-2481, Aug. 2021, doi: 10.1109/LCOMM.2021.3079358.
  27. U. D. Kadiyam and S. Das, “Codes with Availability for Multiple Code Symbols,” in IEEE Communications Letters, vol. 25, no. 8, pp. 2477-2481, Aug. 2021, doi: 10.1109/LCOMM.2021.3079358.
  28. E. Wang, J. Wang, L. Jinghui, Y. Jiarong, Construction of optimal locally repairable codes based on Latin squares, Journal of Beijing University of Posts and Telecommunications, vol. 46, no. 5, pp. 8-14, Oct. 2023, doi: 10.13190/j.jbupt.2022-214
  29. P. Farkaš, “Scalable Family of Codes with Locality and Availability for Information Repair in Distributed Storage Systems,” 2019 4th International Conference on Smart and Sustainable Technologies (SpliTech), Split, Croatia, 2019, pp. 1-4, doi: 10.23919/SpliTech.2019.8783148.
  30. V. I. Shynkarenko, “Constructive-synthesizing representation of geometric fractals,” Cybernetics and Systems Analysis, Vol. 55, No. 2, March, 2019, pp. 186-199, doi: 10.1007/s10559-019-00123-w
  31. V. Shynkarenko, O. Letuchyi and R. Chyhir, “Constructive-synthesizing modeling of fractal crystal lattices,” 2023 IEEE 18th International Conference on Computer Science and Information Technologies (CSIT), Lviv, Ukraine, 2023, pp. 1-4, doi: 10.1109/CSIT61576.2023.10324251.
  32. P. Farkaš, “Linear block code with locality and availability inspired by tetrahedron,” Journal of Electrical Engineering, Vol. 75, No. 1, February 2024, pp. 72-76, doi: https://doi.org/10.2478/jee-2024-0010.
DOI: https://doi.org/10.2478/jee-2025-0036 | Journal eISSN: 1339-309X | Journal ISSN: 1335-3632
Language: English
Page range: 356 - 360
Submitted on: May 22, 2025
|
Published on: Aug 6, 2025
In partnership with: Paradigm Publishing Services
Publication frequency: 6 issues per year

© 2025 Peter Farkaš, Katarína Farkašová, Frederik Pavelka, published by Slovak University of Technology in Bratislava
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.