|
|
|
|
References
|
|
| |
| 1. |
Glukhov M. M., Elizarov V. P., Nechaev A. A., Algebra, v. 2, Gelios ARV, Moscow, 2003 |
| 2. |
Kuzmin A. S., Kurakin V. L., Nechaev A. A., Galois rings as application to the codes and linear recurrences (to appear) |
| 3. |
Goltvanitsa M. A., Zaitsev S. N., Nechaev A. A., “Skew linear recurrences of maximal period over Galois rings”, Fundamental and applied mathematics, 17:3 (2011/2012), 5–23 |
| 4. |
Goltvanitsa M. A., Zaitsev S. N., Nechaev A. A., “Skew LRS of maximal period over Galois rings”, Workshop on Current Trends in Cryptology, 2012 |
| 5. |
Kurakin V. L., Kuzmin A. S., Mikhalev A. V., Nechaev A. A., “Linear recurring sequences over ring and modules”, J. Math. Sci., 76:6 (1995), 2793–2915 |
| 6. |
Nechaev A. A., Kuzmin A. S., Kurakin V. L., “Structural, analitical and statistical properties of linear and polylinear recurrent sequences”, Tr. Diskr. Mat., 3, FIZMATLIT, Moscow, 2000, 155–194 |
| 7. |
Kurakin V. L., “Berlekamp–Massey algorithm over finite rings, modules and bimodules”, Discrete mathematics, 10:4 (1998), 3–34 |
| 8. |
Nechaev A. A., “Finite rings with applications”, Handbook of Algebra, 5, ed. M. Hazewinkel, Elsevier B. V., 2008, 213–320 |
| 9. |
Nechaev A. A., “Finite rings of principal ideals”, Mat. USSR-Sb., 20:3 (1973), 364–382 |
| 10. |
McDonald B. R., Finite rings with identity, Markel Dekker, New York, 1974 |
| 11. |
Lidl R., Niederreiter H., Finite fields, Cambridge University Press, 1983 |
| 12. |
Nechaev A. A., “Kerdock's code in cyclic form”, Discrete Math. Appl., 1:4 (1991), 365–384 |
| 13. |
Nechaev A. A., “Linear recurrent sequences over commutative rings”, Discrete Math. Appl., 2:6 (1992), 659–683 |
| 14. |
Nechaev A. A., “Cycle types of linear substitutions over finite commutative rings”, Russian Acad. Sci. Sb. Math., 78:2 (1994), 283–311 |
| 15. |
Kurakin V. L., Kuzmin A. S., Mikhalev A. V., Nechaev A. A., “Linear recurring sequences over rings and modules”, Journal of Mathematical Sciences, 76:6 (1995), 2793–2915 |
| 16. |
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 |
| 17. |
Tsaban B., Vishne U., “Efficient linear feedback shift registers with maximal period”, Finite Fields and Their Appl., 8:2 (2002), 256–267 |
| 18. |
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 |
| 19. |
Zeng G., He K. C., Han W., “A trinomial type of $\sigma$-LFSR oriented toward software implementation”, Science in China, Series F-Inf. Sci., 50:3 (2007), 359–372 |
| 20. |
Zeng G., Yang Y., Han W., Fan S., “Word oriented cascade jump $\sigma$-LFSR”, AAECC 2009, LNCS, 5527, 2009, 127–136 |
| 21. |
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 |
| 22. |
Ghorpade S. R., Ram S., “Block companion Singer cycles, primitive recursive vector sequences, and coprime polynomial pairs over finite fields”, Finite Fields and Their Appl., 17:5 (2011), 461–472 |