A Graph-Theoretical Method for Decoding Some Group MLD-Codes
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G. C. Clark, Jr., and J. B. Cain, Error-Correction Coding for Digital Communications (Radiosvyaz’, Moscow, 1981) [in Russian].
V. M. Sidel’nikov, “Open Encryption Based on Binary Reed–Muller Codes,” Diskret. Mat. 6 (2), 3–20 (1994).
K.-Kh. Tsimmerman, Methods of Modular Representation Theory in Algebraic Coding Theory (MTsNMO, Moscow, 2011) [in Russian].
“NIST Reveals 26 Algorithms Advancing to the Post-Quantum Crypto ’Semifinals’,” National Institute of Standards and Technology. Jan. 30, 2019. http://nist.gov/news-events/news/2019/01/nist-reveals-26- algorithms-advancing-post-quantum-crypto-semifinals.
M. A. Borodin and I. V. Chizhov, “Effective Attack on the McEliece Cryptosystem Based on Reed-Muller Codes,” Discrete Math. Appl. 26 (1), 273–280 (2014).
L. Minder and A. Shokrollahi, “Cryptanalysis of the Sidelnikov Cryptosystem,” in Advances in Cryptology—EUROCRYPT 2007: Proceedings of 26th Annual International Conference on Theory and Applications of Cryptography Techniques (Barcelona, Spain, May 20–24, 2007) (Springer, Heidelberg, 2007), pp. 347–360 [Lecture Notes in Computer Science, Vol. 4515].
V. M. Sidel’nikov and S. O. Shestakov, “On an Encoding System Constructed on the Basis of Generalized Reed–Solomon Codes,” Discrete Math. Appl. 2 (4), 439–444 (1992).
C. Wieschebrink, “Cryptanalysis of the Niederreiter Public Key Scheme Based on GRS Subcodes,” Post-Quantum Cryptography:Proceedings of the Third International Workshop (Darmstadt, Germany, May 25–28, 2010) (Springer, Heidelberg, 2010), pp. 61–72 [Lecture Notes in Computer Science, Vol. 6061].
V. M. Deundyak and Y. V. Kosolapov, “Cryptosystem Based on Induced Group Codes,” Model. Anal. Inform. Sist. 23 (2), 137–152 (2016).
V. M. Deundyak, Y. V. Kosolapov, and E. A. Lelyuk, “Decoding the Tensor Product of MLD Codes and Applications to Code Cryptosystems,” Model. Anal. Inform. Sist.24 (2), 239–252 (2017) [Automat. Control and Comput. Sci. 52 (7), 647–657, 2018].
T. Kasami and S. Lin, “On the Construction of a Class of Majority-Logic Decodable Codes,” IEEE Trans. Inform. Theory IT-17 (5), 600–610 (1971).
V. M. Sidel’nikov, Coding Theory (Fizmatlit, Moscow, 2008) [in Russian].
V. M. Deundyak and Y. V. Kosolapov, “Algorithms for Majority Decoding of Group Codes,” Model. Anal. Inform. Sist. 22 (4), 464–482 (2015).
E. L. Blokh and V. V. Zyablov, “Coding of Generalized Concatenated Codes,” Problemy Peredachi Informatsii 10 (3), 45–50 (1974).
V. A. Zinov’ev, “Generalized Concatenated Codes,” Problemy Peredachi Informatsii 12 (1), 5–15, (1976).
C. W. Curtis and I. Reiner, Representation Theory of Finite Groups and Associative Algebras (Interscience Publ., New York, 1962).