Random construction of partial MDS codes

1. Blaum M., Hafner J.L., Hetzler S.: Partial-MDS codes and their application to RAID type of architectures. IEEE Trans. Inform. Theory 59(7), 4510–4519 (2013). https://doi.org/10.1109/TIT.2013.2252395.

   Article  MathSciNet  MATH  Google Scholar 

2. Blaum M., Plank J.S., Schwartz M., Yaakobi E.: Partial MDS (PMDS) and sector-disk (SD) codes that tolerate the erasure of two random sectors. In: 2014 IEEE International Symposium on Information Theory, pp. 1792–1796 (2014). https://doi.org/10.1109/ISIT.2014.6875142.

3. Blaum M., Plank J.S., Schwartz M., Yaakobi E.: Construction of partial MDS and sector-disk codes with two global parity symbols. IEEE Trans. Inform. Theory 62(5), 2673–2681 (2016). https://doi.org/10.1109/TIT.2016.2536720.

   Article  MathSciNet  MATH  Google Scholar 

4. Calis G., Koyluoglu O.O.: A general construction for PMDS codes. IEEE Commun. Lett. 21(3), 452–455 (2017). https://doi.org/10.1109/LCOMM.2016.2627569.

   Article  Google Scholar 

5. Chen J., Shum K.W., Yu Q., Sung C.W.: Sector-disk codes and partial MDS codes with up to three global parities. In: 2015 IEEE International Symposium on Information Theory (ISIT), pp. 1876–1880 (2015). https://doi.org/10.1109/ISIT.2015.7282781.

6. Chen M., Huang C., Li J.: On the maximally recoverable property for multi-protection group codes. In: 2007 IEEE International Symposium on Information Theory (ISIT), pp. 486–490 (2007). https://doi.org/10.1109/ISIT.2007.4557272.

7. Gabidulin E.M.: Theory of codes with maximum rank distance. Probl. Inf. Transm. 21(1), 3–16 (1985).

   MathSciNet  MATH  Google Scholar 

8. Gopalan P., Huang C., Jenkins B., Yekhanin S.: Explicit maximally recoverable codes with locality. IEEE Trans. Inform. Theory 60(9), 5245–5256 (2014). https://doi.org/10.1109/TIT.2014.2332338.

   Article  MathSciNet  MATH  Google Scholar 

9. Guruswami V., Jin L., Xing C.: Constructions of maximally recoverable local reconstruction codes via function fields. ArXiv E-prints. arXiv:1808.04539 (2018).

10. Hartshorne R.: Algebraic Geometry, vol. 52. Springer, Berlin (2013).

    MATH  Google Scholar 

11. Horlemann-Trautmann A.L., Marshall K.: New criteria for MRD and Gabidulin codes and some rank-metric code constructions. Adv. Math. Commun. 11(3), 533–548 (2017).

    Article  MathSciNet  Google Scholar 

12. Horlemann-Trautmann A.L., Neri A.: A complete classification of partial-MDS (maximally recoverable) codes with one global parity. Adv. Math. Commun. 14(1), 69–88 (2020). https://doi.org/10.3934/amc.2020006.

    Article  MathSciNet  MATH  Google Scholar 

13. Lewin D., Vadhan S.: Checking polynomial identities over any field: towards a derandomization? In: Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing, pp. 438–447. ACM (1998).

14. Neri A., Horlemann-Trautmann A.L., Randrianarisoa T., Rosenthal J.: On the genericity of maximum rank distance and Gabidulin codes. Des. Codes Cryptogr. 86(2), 341–363 (2018).

    Article  MathSciNet  Google Scholar 

15. Roth R.: Maximum-rank array codes and their application to crisscross error correction. IEEE Trans. Inform. Theory 37(2), 328–336 (1991). https://doi.org/10.1109/18.75248.

    Article  MathSciNet  MATH  Google Scholar 

16. Schwartz J.T.: Fast probabilistic algorithms for verification of polynomial identities. J. ACM 27(4), 701–717 (1980).

    Article  MathSciNet  Google Scholar 

17. Sheekey J.: A new family of linear maximum rank distance codes. Adv. Math. Commun. 10(3), 475–488 (2016).

    Article  MathSciNet  Google Scholar 

Download references