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JOURNALS // Matematicheskie Voprosy Kriptografii [Mathematical Aspects of Cryptography]

Mat. Vopr. Kriptogr., 2015, Volume 6, Issue 2, Pages 19–27 (Mi mvk141)

Digit sequences of skew linear recurrences of maximal period over Galois rings
M. A. Goltvanitsa

References

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  crossref  mathscinet  zmath
2. Nechaev A. A., “Kerdock code in a cyclic form”, Diskretnaya matematika, 1:4 (1989), 123–139 (in Russian)  mathnet  mathscinet  zmath
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  mathnet  crossref  mathscinet  zmath
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  mathscinet  zmath
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  mathnet  mathscinet
6. Tsaban B., Vishne U., “Efficient linear feedback shift registers with maximal period”, Finite Fields and Their Applications, 8:2 (2002), 256–267  crossref  mathscinet  zmath  isi
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  mathscinet  zmath  isi
9. Zeng G., Yang Y., Han W., Fan Sh., “Word oriented cascade jump $\sigma$-LFSR”, AAECC, 2009, 127–136  mathscinet  zmath
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  crossref  mathscinet  zmath  isi
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  crossref  mathscinet  zmath  isi
12. Kuzmin A. S., Nechaev A. A., “Linear recurring sequences over Galois rings”, Uspekhi matem. nauk, 48:1 (1993), 167–168 (in Russian)  mathnet  mathscinet  zmath
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)  mathnet  mathscinet  zmath
15. Kuzmin A. S. Nechaev A. A., “Linear recurring sequences over Galois rings”, Algebra i Logika, 3:2 (1995), 169–189 (in Russian)  mathscinet
16. Lidl R., Niederreiter H., Finite Fields, Encyclopedia of Mathematics and its Applications, 20, Cambridge University Press, 1983  mathscinet  zmath
17. Nechaev A. A., “Finite Rings with Applications”, Handbook of Algebra, 5, ed. M. Hazewinkel, Elsevier B. V., 2008, 213–320  mathscinet  zmath


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