Geodesic
$2$-linear shift register over the Galois ring of even characteristic
Matematičeskie voprosy kriptografii, Tome 3 (2012) no. 2, pp. 27-61 Cet article a éte moissonné depuis la source Math-Net.Ru

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Output sequence properties of self-controlled 2-linear shift register over the Galois ring of even characteristic are investigated. It is shown that almost all initial values generate the output sequence with large linear complexity and maximal possible period for a wide class of control functions and proper choice of an output function. Frequency characteristics of this sequence are close to that of a uniform one. 
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O. A. Kozlitin. $2$-linear shift register over the Galois ring of even characteristic. Matematičeskie voprosy kriptografii, Tome 3 (2012) no. 2, pp. 27-61. http://geodesic.mathdoc.fr/item/MVK_2012_3_2_a1/

[1] Kozlitin O. A., “Periodicheskie svoistva prosteishego 2-lineinogo registra sdviga”, Diskretnaya matematika, 19:3 (2007), 51–78 | MR | Zbl

[2] Kozlitin O. A., “Svoistva vykhodnoi posledovatelnosti prosteishego camoupravlyaemogo 2-lineinogo registra sdviga”, Diskretnaya matematika, 19:4 (2007), 70–96 | MR | Zbl

[3] Kozlitin O. A., “Periodicheskie svoistva 2-lineinogo registra sdviga nad koltsom Galua”, Obozrenie prikladnoi i promyshlennoi matematiki, 18:4 (2011), 513–526 | MR

[4] Kuzmin A. S., Nechaev A. A., “Lineinye rekurrentnye posledovatelnosti nad koltsami Galua”, Algebra i logika, 34:2 (1995), 169–189 | MR

[5] Lidl R., Niderraiter G., Konechnye polya, Mir, M., 1988, 818 pp. | MR | Zbl

[6] Nechaev A. A., “Mnogomernye registry sdviga i slozhnost multiposledovatelnostei”, Trudy po diskretnoi matematike, 6, FIZMATLIT, M., 2002, 150–164

[7] Nechaev A. A., “O podobii matrits nad kommutativnym lokalnym artinovym koltsom”, Trudy seminara imeni I. G. Petrovskogo, 9, 1983, 81–101 | MR | Zbl

[8] Nechaev A. A., “Tsiklovye tipy lineinykh podstanovok nad konechnymi kommutativnymi koltsami”, Matematicheskii sbornik, 184:3 (1993), 21–56 | MR | Zbl

[9] Fomichev V. M., Diskretnaya matematika i kriptologiya, Dialog-MIFI, M., 2003, 397 pp.

[10] Kurakin V. L., Kuzmin A. S., Mikhalev A. V., Nechaev A. A., “Linear recurring sequences over rings and modules”, J. Math. Sciences, 76:6 (1995), 2793–2915 | DOI | MR | Zbl

[11] McEliece R. J., “Irreducible cyclic codes and Gauss sums”, Combinatorics, eds. M. Hall (Jr.), J. H. van Lint, 1975, 185–202 | MR

[12] Nomura T., Fukuda A., “Linear recurring planes and two-dimensional cyclic codes”, Electronic Commun. Japan, 54:3 (1971), 23–30 | MR