@article{MVK_2015_6_2_a2,
author = {M. A. Goltvanitsa},
title = {Digit sequences of skew linear recurrences of maximal period over {Galois} rings},
journal = {Matemati\v{c}eskie voprosy kriptografii},
pages = {19--27},
year = {2015},
volume = {6},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/MVK_2015_6_2_a2/}
}
M. A. Goltvanitsa. Digit sequences of skew linear recurrences of maximal period over Galois rings. Matematičeskie voprosy kriptografii, Tome 6 (2015) no. 2, pp. 19-27. http://geodesic.mathdoc.fr/item/MVK_2015_6_2_a2/
[1] Kurakin V. L., Kuzmin A. S., Mikhalev A. V., Nechaev A. A., “Linear recurring sequences over rings and modules”, J. Math. Sci., 76:6 (1995), 2793–2915 | DOI | MR | Zbl
[2] Nechaev A. A., “Kerdock code in a cyclic form”, Diskretnaya matematika, 1:4 (1989), 123–139 (in Russian) | MR | Zbl
[3] Goltvanitsa M. A., Nechaev A. A., Zaitsev S. N., “Skew linear recurring sequences of maximal period over Galois rings”, J. Math. Sci., 187:2 (2012), 115–128 | DOI | MR | Zbl
[4] Kurakin V. L., Mikhalev A. V., Nechaev A. A., Tsypyschev V. N., “Linear and polylinear recurring sequences over abelian groups and modules”, J. Math. Sci., 102:6 (2000), 4598–4626 | MR | Zbl
[5] Goltvanitsa M. A., Nechaev A. A., Zaitsev S. N., “Skew LRS of maximal period over Galois rings”, Matematicheskie voprosy kriptografii, 4:2 (2013), 59–72 | MR
[6] Tsaban B., Vishne U., “Efficient linear feedback shift registers with maximal period”, Finite Fields and Their Applications, 8:2 (2002), 256–267 | DOI | MR | Zbl
[7] Zeng G., Han W., He K., Word-oriented feedback shift register: $\sigma$-LFSR, Cryptology ePrint Archive: Report 2007/114, http://eprint.iacr.org/2007/114
[8] Zeng G., He K. C., Han W., “A trinomial type of $\sigma$-LFSR oriented toward software implementation”, Science in China, Series F – Information Sciences, 50:3 (2007), 359–372 | MR | Zbl
[9] Zeng G., Yang Y., Han W., Fan Sh., “Word oriented cascade jump $\sigma$-LFSR”, AAECC, 2009, 127–136 | MR | Zbl
[10] Ghorpade S. R., Hasan S. U., Kumari M., “Primitive polynomials, Singer cycles, and word-oriented linear feedback shift registers”, Des. Codes Cryptogr., 58:2 (2011), 123–134 | DOI | MR | Zbl
[11] Ghorpade Sudhir R., Ram Samrith, “Block companion Singer cycles, primitive recursive vector sequences, and coprime polynomial pairs over finite fields”, Finite Fields Appl., 17:5 (2011), 461–472 | DOI | MR | Zbl
[12] Kuzmin A. S., Nechaev A. A., “Linear recurring sequences over Galois rings”, Uspekhi matem. nauk, 48:1 (1993), 167–168 (in Russian) | MR | Zbl
[13] Glukhov M. M., Elizarov V. P., Nechaev A. A., Algebra, v. II, Gelios ARV, 2003 (in Russian)
[14] Kurakin V. L., “The first coordinate sequence of a linear recurrence of maximum period over a Galois ring”, Diskretnaya matematika, 6:2 (1994), 88–100 (in Russian) | MR | Zbl
[15] Kuzmin A. S. Nechaev A. A., “Linear recurring sequences over Galois rings”, Algebra i Logika, 3:2 (1995), 169–189 (in Russian) | MR
[16] Lidl R., Niederreiter H., Finite Fields, Encyclopedia of Mathematics and its Applications, 20, Cambridge University Press, 1983 | MR | Zbl
[17] Nechaev A. A., “Finite Rings with Applications”, Handbook of Algebra, 5, ed. M. Hazewinkel, Elsevier B. V., 2008, 213–320 | MR | Zbl