Voir la notice de l'article provenant de la source Math-Net.Ru
@article{DA_2018_25_1_a4, author = {A. V. Kutsenko}, title = {The {Hamming} distance spectrum between self-dual {Maiorana--McFarland} bent functions}, journal = {Diskretnyj analiz i issledovanie operacij}, pages = {98--119}, publisher = {mathdoc}, volume = {25}, number = {1}, year = {2018}, language = {ru}, url = {https://geodesic-test.mathdoc.fr/item/DA_2018_25_1_a4/} }
TY - JOUR AU - A. V. Kutsenko TI - The Hamming distance spectrum between self-dual Maiorana--McFarland bent functions JO - Diskretnyj analiz i issledovanie operacij PY - 2018 SP - 98 EP - 119 VL - 25 IS - 1 PB - mathdoc UR - https://geodesic-test.mathdoc.fr/item/DA_2018_25_1_a4/ LA - ru ID - DA_2018_25_1_a4 ER -
A. V. Kutsenko. The Hamming distance spectrum between self-dual Maiorana--McFarland bent functions. Diskretnyj analiz i issledovanie operacij, Tome 25 (2018) no. 1, pp. 98-119. https://geodesic-test.mathdoc.fr/item/DA_2018_25_1_a4/
[1] N. A. Kolomeec, A. V. Pavlov, “Properties of bent functions with minimal distance”, Prikl. Diskretn. Mat., 2009, no. 4, 5–20
[2] O. A. Logachev, A. A. Sal'nikov, S. V. Smyshlyaev, V. V. Yashchenko, Boolean functions in coding theory and cryptology, MTsNMO, Moscow, 2012 | MR
[3] F. J. MacWilliams, N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland Math. Libr., 16, North-Holland, Amsterdam, 1977 | MR
[4] A. K. Oblaukhov, “Metric complements to subspaces in the Boolean cube”, J. Appl. Ind. Math., 10:3 (2016), 397–403 | DOI | DOI | MR
[5] V. N. Potapov, “Cardinality spectra of components of correlation immune functions, bent functions, perfect colorings, and codes”, Probl. Inf. Transm., 48:1 (2012), 47–55 | DOI | MR
[6] N. N. Tokareva, “On decomposition of a dual bent function into sum of two bent functions”, Prikl. Discretn. Mat., 2014, no. 4, 59–61
[7] Budaghyan L., Carlet C., Helleseth T., Kholosha A., Mesnager S., “Further results on Niho bent functions”, IEEE Trans. Inf. Theory, 58:11 (2012), 6979–6985 | DOI | MR
[8] Carlet C., “Boolean functions for cryptography and error-correcting codes”, Boolean models and methods in mathematics, computer science, and engineering, Encycl. Math. Appl., 134, Cambridge Univ. Press, New York, 2010, 257–397
[9] Carlet C., Danielson L. E., Parker M. G., Solé P., “Self-dual bent functions”, Int. J. Ifnorm. Coding Theory, 1:4 (2010), 384–399 | DOI | MR
[10] Cusick T. W., Stănică P., Cryptographic Boolean functions and applications, Acad. Press, London, 2017, 288 pp. | MR
[11] Feulner T., Sok L., Solé P., Wassermann A., “Towards the classification of self-dual bent functions in eight variables”, Des. Codes Cryptogr., 68:1 (2013), 395–406 | DOI | MR
[12] Hou X.-D., “On the coefficients of binary bent functions”, Proc. Amer. Math. Soc., 128:4 (2000), 987–996 | DOI | MR
[13] Hou X.-D., “Classification of self dual quadratic bent functions”, Des. Codes Cryptogr., 63:2 (2012), 183–198 | DOI | MR
[14] Kolomeec N.A., “The graph of minimal distances of bent functions and its properties”, Des. Codes Cryptogr., 85:3 (2017), 395–410 | DOI | MR
[15] Kolomeec N. A., Pavlov A. V., “Bent functions on the minimal distance”, Proc. IEEE Region 8th Int. Conf. Computational Technologies in Electrical and Electronics Engineering, SIBIRCON 2010 (Irkutsk, Russia, July 11–15, 2010), IEEE, Piscataway, 2010, 145–149
[16] Langevin P., Leander G., “Monomial bent functions and Stickelberger's theorem”, Finite Fields Appl., 14:3 (2008), 727–742 | DOI | MR
[17] McFarland R.L., “A family of difference sets in non-cyclic groups”, J. Comb. Theory Ser. A, 15:1 (1973), 1–10 | DOI | MR
[18] Mesnager S., “Several new infinite families of bent functions and their duals”, IEEE Trans. Inf. Theory, 60:7 (2014), 4397–4407 | DOI | MR
[19] Rothaus O., “On “bent” functions”, J. Comb. Theory Ser. A, 20:3 (1976), 300–305 | DOI | MR
[20] Tokareva N. N., “Duality between bent functions and affine functions”, Discrete Math., 312:3 (2012), 666–670 | DOI | MR
[21] Tokareva N. N., Bent functions: Results and applications to cryptography, Acad. Press, London, 2015, 220 pp. | MR
[22] Xu B., “Dual bent functions on finite groups and $C$-algebras”, J. Pure Appl. Algebra, 220:3 (2016), 1055–1073 | DOI | MR