Research Article
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Year 2022, , 45 - 49, 30.04.2022
https://doi.org/10.30931/jetas.1032180

Abstract

References

  • [1] MacWilliams, F. J., Sloane, N. J. A., "The theory of error-correcting codes", Amsterdam: North-Holland (1977).
  • [2] Hurley, T., "MDS codes over finitefields", arXiv:1903.05265 [cs.IT].
  • [3] Gupta, K. C., Pandey, S. K., Ray, I. G., Samanta, S. "Crypto- graphically significant mds matrices over finite fields: A brief survey and some generalized results", Advances in Mathematics of Communications 13 (4) (2019) : 779-843.
  • [4] Daemen, J., Rijmen, V., "The design of Rijndael: AES - The Advanced Encryption Standard, Springer-Verlag (2002).
  • [5] Hu, Y., Zhang, X., Lee, P. P. C., Zhou, P., "Generalized optimal storage scaling via network coding", IEEE International Symposium on Information Theory - Proceedings, 2018-June, art. no. 8437684 (2018) : 956-960.
  • [6] Guang, X., Yeung, R.W., "Linear network error correction coding revisited", IEEE International Symposium on Information Theory - Proceedings, 2020-June, art. no. 9174493 (2020) : 1635-1640.
  • [7] Wu, X., Li, Q., Leung, V. C. M., Ching, P. C., "Joint Fronthaul multicast and cooperative beam- forming for cache-enabled cloud-based small cell networks: An MDS codes-aided approach", IEEE Transactions on Wireless Communications 18(10) art. no. 8786923 (2019) : 4970-4982.
  • [8] Ko, D., Hong, B., Choi, W. "Probabilistic caching based on maximum distance separable code in a user-centric clustered cache-aided wireless network", IEEE Transactions on Wireless Communications 18(3) art. no. 8638790 (2019) : 1792-1804.
  • [9] Gu, S., Li, J., Wang, Y., Wang, N., Zhang, Q. "DR-MDS: An energy-efficient coding scheme in D2D distributed storage network for the internet of things", IEEE Access 7 art. no. 8648336 (2019) : 24179-24191.
  • [10] Pedersen, J., Graell Amat, A.I., Andriyanova, I., Brannstrom, F. "Optimizing MDS coded caching in wireless networks with device-to-device communication", IEEE Transactions on Wireless Communications 18(1) art. no. 8551275 (2019) : 286-295.
  • [11] Mousavi, S., Zhou, T., Tian, C. "Delayed parity generation in MDS storage codes", IEEE International Symposium on Information Theory - Proceedings 8437700 (2018) : 1889-1893.
  • [12] Heidarpour, A. R., Ardakani, M., Tellambura, C., "Network coded cooperation based on relay selection with imperfect CSI", IEEE Vehicular Technology Conference 2017-September, (2018) : 1-5.
  • [13] Tamo, I., Wang, Z., Bruck, J. "Zigzag codes: MDS array codes with optimal rebuilding", IEEE Transactions on Information Theory 59(3) art. no. 6352912 (2013) : 1597-1616.
  • [14] Guang, X., Fu, F.-W., Zhang, Z. "Construction of network error correction codes in packet networks", IEEE Transactions on Information Theory 59(2) art. no. 6320693, (2013) : 1030-1047.
  • [15] Shah, N. B., Rashmi, K. V., Kumar, P. V., Ramchandran, K. "Interference alignment in regenerating codes for distributed storage: Necessity and code constructions", IEEE Transactions on Information Theory 5(4) art. no. 6096412 (2012) : 2134-2158.
  • [16] Hu, Y., Xu, Y., Wang, X., Zhan, C., Li, P. "Cooperative recovery of distributed storage systems from multiple losses with network coding", IEEE Journal on Selected Areas in Communica tions 28 (2) art. no. 5402494 (2010) : 268-276.
  • [17] Silva, D., Kschischang, F. R. "Security for wiretap networks via rank-metric codes", IEEE International Symposium on Information Theory - Proceedings art. no. 4594971 (2008) : 176-180.
  • [18] Fragouli, C., Soljanin, E. "Information flow decomposition for network coding", IEEE Trans- actions on Information Theory 52(3) (2006) : 829-848.
  • [19] Gupta, K. C., Ray, I. G., "Cryptographically significant MDS matrices based on circulant and circulant-like matrices for lightweight applications", Cryptography and Communications 7 (2015) : 257-287.
  • [20] Liu, M., Sim, S. M., "Lightweight MDS generalized circulant matrices", International Conference on Fast Software Encryption, Lecture Notes in Computer Science 9783 Springer, Berlin, Heidelberg (2016) : 101-120.
  • [21] Sarkar, S., Syed, H., "Lightweight diffusion layer: Importance of Toeplitz matrices", IACR Trans. Symmetric Cryptol. (2016) : 95-113.
  • [22] Sarkar, S., Syed, H., "Analysis of toeplitz MDS matrices", ACISP 2017, LNCS 10343 (2017) : 3-18.

Lifted MDS Codes over Finite Fields

Year 2022, , 45 - 49, 30.04.2022
https://doi.org/10.30931/jetas.1032180

Abstract

MDS codes are elegant constructions in coding theory and have mode important applications in network coding, distributed data storage, communication systems etc. In this study, a method is given which MDS codes are lifted to a higher finite field. The presented method satisfies the protection of the distance and creating the MDS code over the $F_q$ by using MDS code over $F_p.$

References

  • [1] MacWilliams, F. J., Sloane, N. J. A., "The theory of error-correcting codes", Amsterdam: North-Holland (1977).
  • [2] Hurley, T., "MDS codes over finitefields", arXiv:1903.05265 [cs.IT].
  • [3] Gupta, K. C., Pandey, S. K., Ray, I. G., Samanta, S. "Crypto- graphically significant mds matrices over finite fields: A brief survey and some generalized results", Advances in Mathematics of Communications 13 (4) (2019) : 779-843.
  • [4] Daemen, J., Rijmen, V., "The design of Rijndael: AES - The Advanced Encryption Standard, Springer-Verlag (2002).
  • [5] Hu, Y., Zhang, X., Lee, P. P. C., Zhou, P., "Generalized optimal storage scaling via network coding", IEEE International Symposium on Information Theory - Proceedings, 2018-June, art. no. 8437684 (2018) : 956-960.
  • [6] Guang, X., Yeung, R.W., "Linear network error correction coding revisited", IEEE International Symposium on Information Theory - Proceedings, 2020-June, art. no. 9174493 (2020) : 1635-1640.
  • [7] Wu, X., Li, Q., Leung, V. C. M., Ching, P. C., "Joint Fronthaul multicast and cooperative beam- forming for cache-enabled cloud-based small cell networks: An MDS codes-aided approach", IEEE Transactions on Wireless Communications 18(10) art. no. 8786923 (2019) : 4970-4982.
  • [8] Ko, D., Hong, B., Choi, W. "Probabilistic caching based on maximum distance separable code in a user-centric clustered cache-aided wireless network", IEEE Transactions on Wireless Communications 18(3) art. no. 8638790 (2019) : 1792-1804.
  • [9] Gu, S., Li, J., Wang, Y., Wang, N., Zhang, Q. "DR-MDS: An energy-efficient coding scheme in D2D distributed storage network for the internet of things", IEEE Access 7 art. no. 8648336 (2019) : 24179-24191.
  • [10] Pedersen, J., Graell Amat, A.I., Andriyanova, I., Brannstrom, F. "Optimizing MDS coded caching in wireless networks with device-to-device communication", IEEE Transactions on Wireless Communications 18(1) art. no. 8551275 (2019) : 286-295.
  • [11] Mousavi, S., Zhou, T., Tian, C. "Delayed parity generation in MDS storage codes", IEEE International Symposium on Information Theory - Proceedings 8437700 (2018) : 1889-1893.
  • [12] Heidarpour, A. R., Ardakani, M., Tellambura, C., "Network coded cooperation based on relay selection with imperfect CSI", IEEE Vehicular Technology Conference 2017-September, (2018) : 1-5.
  • [13] Tamo, I., Wang, Z., Bruck, J. "Zigzag codes: MDS array codes with optimal rebuilding", IEEE Transactions on Information Theory 59(3) art. no. 6352912 (2013) : 1597-1616.
  • [14] Guang, X., Fu, F.-W., Zhang, Z. "Construction of network error correction codes in packet networks", IEEE Transactions on Information Theory 59(2) art. no. 6320693, (2013) : 1030-1047.
  • [15] Shah, N. B., Rashmi, K. V., Kumar, P. V., Ramchandran, K. "Interference alignment in regenerating codes for distributed storage: Necessity and code constructions", IEEE Transactions on Information Theory 5(4) art. no. 6096412 (2012) : 2134-2158.
  • [16] Hu, Y., Xu, Y., Wang, X., Zhan, C., Li, P. "Cooperative recovery of distributed storage systems from multiple losses with network coding", IEEE Journal on Selected Areas in Communica tions 28 (2) art. no. 5402494 (2010) : 268-276.
  • [17] Silva, D., Kschischang, F. R. "Security for wiretap networks via rank-metric codes", IEEE International Symposium on Information Theory - Proceedings art. no. 4594971 (2008) : 176-180.
  • [18] Fragouli, C., Soljanin, E. "Information flow decomposition for network coding", IEEE Trans- actions on Information Theory 52(3) (2006) : 829-848.
  • [19] Gupta, K. C., Ray, I. G., "Cryptographically significant MDS matrices based on circulant and circulant-like matrices for lightweight applications", Cryptography and Communications 7 (2015) : 257-287.
  • [20] Liu, M., Sim, S. M., "Lightweight MDS generalized circulant matrices", International Conference on Fast Software Encryption, Lecture Notes in Computer Science 9783 Springer, Berlin, Heidelberg (2016) : 101-120.
  • [21] Sarkar, S., Syed, H., "Lightweight diffusion layer: Importance of Toeplitz matrices", IACR Trans. Symmetric Cryptol. (2016) : 95-113.
  • [22] Sarkar, S., Syed, H., "Analysis of toeplitz MDS matrices", ACISP 2017, LNCS 10343 (2017) : 3-18.
There are 22 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Elif Segah Oztas 0000-0003-0032-3400

Publication Date April 30, 2022
Published in Issue Year 2022

Cite

APA Oztas, E. S. (2022). Lifted MDS Codes over Finite Fields. Journal of Engineering Technology and Applied Sciences, 7(1), 45-49. https://doi.org/10.30931/jetas.1032180
AMA Oztas ES. Lifted MDS Codes over Finite Fields. JETAS. April 2022;7(1):45-49. doi:10.30931/jetas.1032180
Chicago Oztas, Elif Segah. “Lifted MDS Codes over Finite Fields”. Journal of Engineering Technology and Applied Sciences 7, no. 1 (April 2022): 45-49. https://doi.org/10.30931/jetas.1032180.
EndNote Oztas ES (April 1, 2022) Lifted MDS Codes over Finite Fields. Journal of Engineering Technology and Applied Sciences 7 1 45–49.
IEEE E. S. Oztas, “Lifted MDS Codes over Finite Fields”, JETAS, vol. 7, no. 1, pp. 45–49, 2022, doi: 10.30931/jetas.1032180.
ISNAD Oztas, Elif Segah. “Lifted MDS Codes over Finite Fields”. Journal of Engineering Technology and Applied Sciences 7/1 (April 2022), 45-49. https://doi.org/10.30931/jetas.1032180.
JAMA Oztas ES. Lifted MDS Codes over Finite Fields. JETAS. 2022;7:45–49.
MLA Oztas, Elif Segah. “Lifted MDS Codes over Finite Fields”. Journal of Engineering Technology and Applied Sciences, vol. 7, no. 1, 2022, pp. 45-49, doi:10.30931/jetas.1032180.
Vancouver Oztas ES. Lifted MDS Codes over Finite Fields. JETAS. 2022;7(1):45-9.