DOI QR코드

DOI QR Code

CIS CODES OVER 𝔽4

  • 투고 : 2020.04.20
  • 심사 : 2020.06.10
  • 발행 : 2020.06.30

초록

We study the complementary information set codes (for short, CIS codes) over 𝔽4. They are strongly connected to correlation-immune functions over 𝔽4. Also the class of CIS codes includes the self-dual codes. We find a construction method of CIS codes over 𝔽4 and a criterion for checking equivalence of CIS codes over 𝔽4. We complete the classification of all inequivalent CIS codes of length up to 8 over 𝔽4.

키워드

참고문헌

  1. W. Bosma, J. Cannon, C. Playoust, The Magma algebra system I: The user language, J. Symbolic Comput 24 (1997), 235-265. https://doi.org/10.1006/jsco.1996.0125
  2. P. Camion, A. Canteaut. Correlation-immune and resilient functions over a finite alphabet and their applications in cryptography, Designs Codes Crypt. 16 (2) (1999), 121-149. https://doi.org/10.1023/A:1008337029047
  3. P. Camion, C. Carlet, P. Charpin, N. Sendrier. On correlation-immune functions, Lecture Notes in Computer Science, 576 (1992), 86-100.
  4. C. Carlet, More correlation-immune and resilient functions over Galois fields and Galois rings, Advances in Cryptology, EUROCRYPT'97, Lecture Note in Computer Sciences, Springer Verlag 1233 (1997), 422-433.
  5. C. Carlet, F. Freibert, S. Guilley, M. Kiermaier, J.-L. Kim, P. Sole, Higher-order CIS codes, IEEE Trans. Inform. Theory 60 (9) (2014), 5283-5295. https://doi.org/10.1109/TIT.2014.2332468
  6. C. Carlet, P. Gaborit, J-L. Kim, P. Sole, A new class of codes for Boolean masking of cryptographic computations, IEEE Trans. Inform. Theory 58 (2012), 6000-6011. https://doi.org/10.1109/TIT.2012.2200651
  7. K. Gopalakrishnan, D. R. Stinson Three characterizations of non-binary correlation-immune and resilient functions, Designs Codes Crypt. 5 (1995), 241-251. https://doi.org/10.1007/BF01388386
  8. M. Harada, The existence of a self-dual [70, 35, 12] code and formally self-dual codes, Finte Fields Appl. 3 (1997), 131-139. https://doi.org/10.1006/ffta.1996.0174
  9. M. Harada, A. Munemasa, Classification of self-dual codes of length 36, Adv. Math. Commun. 6 (2012), 229-235. https://doi.org/10.3934/amc.2012.6.229
  10. H. J. Kim: https://drive.google.com/file/d/1sVZ-Em5hHFs36-hBLGda0NLqmt8RThkh/view?usp=sharing.
  11. H. J. Kim and Y. Lee, Complementary information set codes over GF(p), Designs Codes Crypt. 81 (2016), 541-555. https://doi.org/10.1007/s10623-015-0174-3
  12. H. J. Kim and Y. Lee, t-CIS codes over GF(p) and orthogonal arrays, Discrete Applied Mathematics 217 (2017), 601-612. https://doi.org/10.1016/j.dam.2016.09.032
  13. J.-L. Kim, New extremal self-dual codes of lengths 36, 38 and 58, IEEE Trans. Inform. Theory 47 (2001), 386-393 https://doi.org/10.1109/18.904540
  14. J.-L. Kim and Y. Lee, Euclidean and Hermitian self-dual MDS codes over large finite fields, J. Combin. Theory Ser. A 105 (1) (2004), 79-95. https://doi.org/10.1016/j.jcta.2003.10.003
  15. C.P. Schnorr, S. Vaudenay, Black box cryptanalysis of hash networks based on multipermutations, Advances in Cryptology, EUROCRYPT'94, Lecture Note in Computer Science 950, Springer Verlag (1995), 47-57.
  16. T. Siegenthaler, Correlation-immunity of non-linear Combining functions for cryptographic applications, IEEE Trans. Inform. Theory 30 (5) (1984), 776-780. https://doi.org/10.1109/TIT.1984.1056949