The number of different $r$-patterns in linear recurrent sequences over Galois rings
Matematičeskie voprosy kriptografii, Tome 4 (2013) no. 3, pp. 49-82 Cet article a éte moissonné depuis la source Math-Net.Ru

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The number of different $r$-patterns on the period and on the path of period of linear recurrent sequences over Galois rings is discussed. These results are of interest for the linear recurrent sequences over residue rings of primary order.
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O. V. Kamlovskii. The number of different $r$-patterns in linear recurrent sequences over Galois rings. Matematičeskie voprosy kriptografii, Tome 4 (2013) no. 3, pp. 49-82. http://geodesic.mathdoc.fr/item/MVK_2013_4_3_a3/

[1] Alferov A. P., Zubov A. Yu., Kuzmin A. S., Cheremushkin A. V., Osnovy kriptografii, Uchebnoe posobie, Gelios ARV, M., 2001, 480 pp.

[2] Knut D. E., Iskusstvo programmirovaniya, Uchebnoe posobie, v. 2, Izd. dom Vilyams, M., 2000, 832 pp.

[3] Mullen G. L., Shparlinski I. E., “Values of linear recurring sequences of vectors over finite fields”, Acta Arith., 65:3 (1993), 221–226 | MR | Zbl

[4] Bylkov D. N., Kamlovskii O. V., “Indeksy vkhozhdenii elementov v lineinye rekurrentnye posledovatelnosti nad primarnymi koltsami vychetov”, Problemy peredachi informatsii, 44:2 (2008), 101–109 | MR

[5] Kamlovskii O. V., Kuzmin A. S., “Otsenki chastot poyavleniya elementov v lineinykh rekurrentnykh posledovatelnostyakh nad koltsami Galua”, Fundam. i prikl. matematika, 6:4 (2000), 1083–1094 | MR | Zbl

[6] Kuzmin A. S., “Raspredelenie elementov na tsiklakh lineinykh rekurrent nad koltsami vychetov”, Uspekhi matem. nauk, 47:6 (1992), 213–214 | MR | Zbl

[7] Shparlinskii I. E., “O raspredelenii znachenii rekurrentnykh posledovatelnostei”, Problemy peredachi informatsii, 25:2 (1989), 46–53 | MR | Zbl

[8] Chou W. S., Mullen G. L., “Generating linear spans over finite fields”, Acta Arith., 61:2 (1992), 183–191 | MR | Zbl

[9] Shparlinskii I. E., “O chisle prostykh delitelei rekurrentnykh posledovatelnostei”, Matem. zametki, 38:1 (1985), 29–34 | MR | Zbl

[10] Shparlinskii I. E., “O chisle razlichnykh prostykh delitelei rekurrentnykh posledovatelnostei”, Matem. zametki, 42:4 (1987), 494–507 | MR | Zbl

[11] McDonald B. R., Finite rings with identity, Dekker, New York, 1974, 429 pp. | MR | Zbl

[12] Nechaev A. A., “Kod Kerdoka v tsiklicheskoi forme”, Diskretn. matem., 1:4 (1989), 123–139 | MR | Zbl

[13] Lidl R., Niderraiter G., Konechnye polya, v. 1, 2, Mir, M., 1988, 824 pp. | MR | Zbl

[14] Kuzmin A. S., Kurakin V. L., Nechaev A. A., “Psevdosluchainye i polilineinye posledovatelnosti”, Trudy po diskretnoi matematike, 1, TVP, M., 1997, 139–202 | MR | Zbl

[15] Bylkov D. N., “Klass uslozhnenii lineinykh rekurrent nad koltsom Galua, ne privodyaschii k potere informatsii”, Problemy peredachi informatsii, 46:3 (2010), 51–59 | MR | Zbl

[16] Kamlovskii O. V., “Chastotnye kharakteristiki lineinykh rekurrentnykh posledovatelnostei nad koltsami Galua”, Matem. sbornik, 200:4 (2009), 31–52 | DOI | MR | Zbl

[17] Hall M., “Equidistribution of residues in sequences”, Duke Math. J., 4:4 (1938), 691–695 | DOI | MR | Zbl

[18] Laksov D., “Lineinye rekurrentnye posledovatelnosti nad konechnymi polyami”, Matematika. Sbornik perevodov, 11:6 (1967), 145—158

[19] Nechaev A. A., Kuzmin A. S., Kurakin V. L., “Strukturnye, analiticheskie i statisticheskie svoistva lineinykh i polilineinykh rekurrent”, Trudy po diskretnoi matematike, 3, TVP, M., 2000, 155–194

[20] Mikhailov D. A., “Unitarnye polilineinye registry i ikh periody”, Diskretn. matem., 14:1 (2002), 30–59 | DOI | MR | Zbl

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

[22] Kuzmin A. S., Nechaev A. A., “Complete weight enumerators of generalized Kerdock code and related linear codes over Galois ring”, Discr. Appl. Math., 111 (2001), 117–137 | DOI | MR | Zbl

[23] Glukhov M. M., Elizarov V. P., Nechaev A. A., Algebra, v. 2, Gelios ARV, M., 2003, 414 pp.

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

[25] Kurakin V. L., “Polinomialnye preobrazovaniya lineinykh rekurrentnykh posledovatelnostei nad konechnymi kommutativnymi koltsami”, Diskretn. matem., 12:3 (2000), 3–36 | DOI | MR | Zbl

[26] Elizarov V. P., Konechnye koltsa, Gelios ARV, M., 2006, 304 pp.

[27] Shparlinski I. E., “On the distribution of values of recurring sequences and the Bell numbers in finite fields”, European J. Combin., 12 (1991), 81–87 | DOI | MR | Zbl

[28] Tietavainen A., “On the solvability of equations in incomplete finite fields”, Ann. Univ. Turkuensis, 102 (1967), 3–12 | MR

[29] Herlestam T., “On functions of linear shift register sequences”, Lect. Notes Comput. Sci., 219, 1986, 119–129 | DOI | MR | Zbl

[30] Kurakin V. L., “Pervaya koordinatnaya posledovatelnost lineinoi rekurrenty maksimalnogo perioda nad koltsom Galua”, Diskretn. matem., 6:2 (1994), 88–100 | MR | Zbl

[31] Sachkov V. N., Vvedenie v kombinatornye metody diskretnoi matematiki, Nauka, M., 1982, 384 pp. | MR | Zbl