Hadamard square of linear codes and generalized Hamming weight of Reed–Muller codes order 2
Diskretnaya Matematika, Tome 35 (2023) no. 1, pp. 128-152.

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I. V. Chizhov. Hadamard square of linear codes and generalized Hamming weight of Reed–Muller codes order 2. Diskretnaya Matematika, Tome 35 (2023) no. 1, pp. 128-152. http://geodesic.mathdoc.fr/item/DM_2023_35_1_a8/

[1] Pellikaan R., “On decoding by error location and dependent sets of error positions”, Discrete Mathematics, 106–107 (1992), 369–381 | DOI | MR

[2] Chen H., Cramer R., “Algebraic geometric secret sharing schemes and secure multi-party computations over small fields”, CRYPTO 2006, Lect. Notes Comput. Sci., 4117, 2006, 521–536 | DOI | MR

[3] Borodin M. A., Chizhov I. V., “Effektivnaya ataka na kriptosistemu Mak-Elisa, postroennuyu na osnove kodov Rida–Mallera”, Diskretnaya matematika, 26:1 (2014), 10–20

[4] Wieschebrink C., “Cryptanalysis of the Niederreiter public key scheme based on GRS subcodes”, PQCrypto 2010, Lect. Notes Comput. Sci., 6061, 2010, 61–72 | DOI | MR

[5] Couvreur C., Gaborit P., Gauthier-Umaña V., Otmani A., Tillich J.-P., “Distinguisher-based attacks on public-key cryptosystems using Reed–Solomon codes”, Des. Codes Cryptogr., 73:2 (2014), 641–666 | DOI | MR

[6] Couvreur A., Márquez-Corbella I., Pellikaan R., “Cryptanalysis of public-key cryptosystems that use subcodes of algebraic geometry codes”, Coding Theory and Applications, CIM Ser. in Math. Sci., 3, Springer, Cham, 2015, 133–140 | DOI | MR

[7] Couvreur A., Otmani A., Tillich J.-P., “Polynomial time attack on wild McEliece over quadratic extensions”, IEEE Trans. Inf. Theory, 63:1 (2017), 404–427 | DOI | MR

[8] Couvreur A., Otmani A., Tillich J.-P., Gauthier-Umaña V., “A polynomial-time attack on the BBCRS scheme”, PKC 2015, Lect. Notes Comput. Sci., 9020, 2015, 175–193 | DOI | MR

[9] Otmani A., Kalachi H. T., “Square code attack on a modified Sidelnikov cryptosystem”, C2SI 2015, Lect. Notes Comput. Sci., 9084, 2015, 173–183 | DOI | MR

[10] Faugére J., Gauthier-Umaña V., Otmani A., Perret L., Tillich J.-P., “A distinguisher for high-rate McEliece cryptosystems”, IEEE Trans. Inf. Theory, 59:10 (2013), 6830–6844 | DOI | MR

[11] Cascudo I., Cramer R., Mirandola D., Zémor G., “Squares of random linear codes”, IEEE Trans. Inf. Theory, 61:3 (2015), 1159–1173 | DOI | MR

[12] Bardet M., Bertin M., Couvreur A., Otmani A., “Practical algebraic attack on DAGS”, CBC 2019, Lect. Notes Comput. Sci., 11666, 2019, 86–101 | DOI

[13] Mak-Vilyams F. Dzh., Sloen N. Dzh. A., Teoriya kodov, ispravlyayuschikh oshibki, Svyaz, M., 1979, 744 pp.

[14] Hall J. I., Notes on Coding Theory, Chapter 3: Linear Codes, 2010 https://users.math.msu.edu/users/halljo/classes/CODENOTES/Linear.pdf

[15] Heijnen P., Pellikaan R., “Generalized Hamming weights of $q$-ary Reed–Muller codes”, IEEE Trans. Inf. Theory, 44:1 (1998), 181–196 | DOI | MR

[16] Randriambololona H., “On products and powers of linear codes under componentwise multiplication”, AGCT 2013, Contemp. Math., 637, 2015, 3–78 | DOI | MR

[17] Wei V. K., “Generalized Hamming weights for linear codes”, IEEE Trans. Inf. Theory, 37:5 (1991), 1412–1418 | DOI | MR

[18] Delsarte P., Goethals J. M., Mac Williams F. J., “On generalized Reed–Muller codes and their relatives”, Inf. Control, 16:5 (1970), 403–442 | DOI | MR

[19] Abbe E., Shpilka A., Wigderson A., “Reed–Muller codes for random erasures and errors”, STOC'15: Proc. 47th Ann. ACM Symp. Theory Comput., Assoc. Comput. Mach., New York, 2015, 297–306 | MR