Korean J. Math. Vol. 28 No. 2 (2020) pp.285-294
DOI: https://doi.org/10.11568/kjm.2020.28.2.285

CIS codes over ${\mathbb F}_4$

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Published: Jun 30, 2020
Keywords:
complementary information set code, self-dual code, equivalence, correlation-immune
Mathematics Subject Classification:
94B05, 11T71

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Hyun Jin Kim
University College Yonsei University Incheon 21983, Republic of Korea

Abstract

We study the complementary information set codes (for short, CIS codes) over ${\mathbb F}_4$. They are strongly connected to correlation-immune functions over ${\mathbb F}_4$. Also the class of CIS codes includes the self-dual codes. We find a construction method of CIS codes over ${\mathbb F}_4$ and a criterion for checking equivalence of CIS codes over ${\mathbb F}_4$. We complete the classification of all inequivalent CIS codes of length up to $8$ over ${\mathbb F}_4$.


Article Details

Supporting Agencies

the National Research Foundation of Korea

References

[1] W. Bosma, J. Cannon, C. Playoust, The Magma algebra system I: The user language, J. Symbolic Comput 24 (1997), 235–265. Google Scholar

[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. Google Scholar

[3] P. Camion, C. Carlet, P. Charpin, N. Sendrier. On correlation-immune functions, Lecture Notes in Computer Science, 576 (1992), 86–100. Google Scholar

[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. Google Scholar

[5] C. Carlet, F. Freibert, S. Guilley, M. Kiermaier, J.-L. Kim, P. Sol e, Higher-order CIS codes, IEEE Trans. Inform. Theory 60 (9) (2014), 5283-5295. Google Scholar

[6] C. Carlet, P. Gaborit, J-L. Kim, P. Sol e, A new class of codes for Boolean masking of cryptographic computations, IEEE Trans. Inform. Theory 58 (2012), 6000-6011. Google Scholar

[7] K. Gopalakrishnan, D. R. Stinson Three characterizations of non-binary correlation-immune and resilient functions, Designs Codes Crypt. 5 (1995), 241– 251. Google Scholar

[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. Google Scholar

[9] M. Harada, A. Munemasa, Classification of self-dual codes of length 36, Adv. Math. Commun. 6 (2012), 229–235. Google Scholar

[10] H. J. Kim: https://drive.google.com/file/d/1sVZ-Em5hHFs36-hBLGda0NLqmt8 RThkh/view?usp=sharing. Google Scholar

[11] H. J. Kim and Y. Lee, Complementary information set codes over GF(p), Designs Codes Crypt. 81 (2016), 541–555. Google Scholar

[12] H. J. Kim and Y. Lee, t-CIS codes over GF (p) and orthogonal arrays, Discrete Applied Mathematics 217 (2017), 601–612. Google Scholar

[13] J.-L. Kim, New extremal self-dual codes of lengths 36, 38 and 58, IEEE Trans. Inform. Theory 47 (2001), 386–393. Google Scholar

[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. Google Scholar

[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. Google Scholar

[16] T. Siegenthaler, Correlation-immunity of non-linear Combining functions for cryptographic applications, IEEE Trans. Inform. Theory 30 (5) (1984), 776–780. Google Scholar