Geodesic
Recursively-generated permutations of a binary space
Matematičeskie voprosy kriptografii, Tome 5 (2014) no. 2, pp. 7-20 Cet article a éte moissonné depuis la source Math-Net.Ru

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Nonlinear permutations of a vector space $GF(2)^m$ of any dimension $m\ne2^t$, $t\in\mathbb N$, induced by iterations of linear transformation over the ring $R=\mathbb Z_4$ with characteristic polynomial $F(x)\in R[x]$, $F(x)\equiv(x\oplus e)^m\pmod2$, are studied. 
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A. V. Abornev. Recursively-generated permutations of a binary space. Matematičeskie voprosy kriptografii, Tome 5 (2014) no. 2, pp. 7-20. http://geodesic.mathdoc.fr/item/MVK_2014_5_2_a1/

[1] Nechaev A. A., Abornev A. V., “Nonlinear permutations on a space over a finite field induced by linear transformations of a module over a Galois ring”, Mathematical Aspects of Cryptography, 4:2 (2013), 81–100

[2] Kuzmin A. S., Nechaev A. A., “Linear recurring sequences over Galois rings”, Algebra and Logic, 34:2 (1995), 87–100 | DOI | MR

[3] Nechaev A. A., “On the structure of finite commutative rings with an identity”, Mathematical Notes, 10:6 (1971), 840–845 | DOI | MR | Zbl

[4] Elizarov V. P., Finite Rings (foundations of the theory), Gelios-ARV, Moscow, 2006, 304 pp. (in Russian)

[5] Nechaev A. A., “Finite rings with applications”, Handbook of Algebra, 5, ed. M. Hazewinkel, Elsevier, 2008, 213–320 | DOI | MR | Zbl

[6] Greferath M., Nechaev A., “Generalized Frobenius extensions of finite rings and trace functions”, Information Theory Workshop (ITW), IEEE, Dublin, 2010, 1–5

[7] Edwards A. W. F., Pascal's Arithmetical Triangle: The Story of a Mathematical Idea, Charles Griffin, London, 1987 | MR | Zbl

[8] Call G. S., Vellman D. J., “Pascal's matrices”, Amer. Math. Monthly, 100 (1993), 372–376 | DOI | MR | Zbl

[9] Edelman A., Strang G., “Pascal matrices”, Amer. Math. Monthly, 111:3 (2004), 361–385 | DOI | MR

[10] Glukhov M. M., Elizarov V. P., Nechaev A. A., Algebra, v. II, Gelios-ARV, Moscow, 2003, 416 pp. (in Russian)

[11] Jonathan L. G., Combinatorial Methods with Computer Applications, Discrete Mathematics and Its Applications, Chapman and Hall/CRC, 2007, 664 pp. | MR