Equidistributed sequences over finite fields produced by one class of linear recurring sequences over residue rings

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• 作者：O. V. Kamlovskii (1)
  
• 刊名：Problems of Information Transmission
• 出版年：2014
• 出版时间：April 2014
• 年：2014
• 卷：50
• 期：2
• 页码：171-185
• 全文大小：428 KB
• 参考文献：1. Lidl, R. and Niederreiter, H., / Finite Fields, Reading: Addison-Wesley, 1983. Translated under the title / Konechnye polya, 2 vols., Moscow: Mir, 1988.
  2. Glukhov, M.M., Elizarov, V.P., and Nechaev A.A., / Algebra, Moscow: Gelios ARV, 2003, Part 2.
  3. Kurakin, V.L., Kuzmin, A.S., Mikhalev, A.V., and Nechaev, A.A., Linear Recurring Sequences over Rings and Modules, / J. Math. Sci., 1995, vol. 76, no. 6, pp. 2793鈥?915. CrossRef
  4. Bumby, R.T., A Distribution Property for Linear Recurrence of the Second Order, / Proc. Amer. Math. Soc., 1975, vol. 50, pp. 101鈥?06. CrossRef
  5. Knight, M.J. and Webb, W.A., Uniform Distribution of Third Order Linear Recurrence Sequences, / Acta Arith., 1980, vol. 36, no. 1, pp. 7鈥?0.
  6. Niederreiter, H. and Shiue, J.-S., Equidistribution of Linear Recurring Sequences in Finite Fields. II, / Acta Arith., 1980/81, vol. 38, no. 2, pp. 197鈥?07.
  7. Narkiewicz, W., / Uniform Distribution of Sequences of Integers in Residue Classes, Lect. Notes Math., vol. 1087, Berlin: Springer, 1984.
  8. Tichy, R.F. and Turnwald, G., Uniform Distribution of Recurrence in Dedekind Domains, / Acta Arith., 1985, vol. 46, no. 1, pp. 81鈥?9.
  9. Turnwald, G., Uniform Distribution of Second-Order Linear Recurring Sequences, / Proc. Amer. Math. Soc., 1986, vol. 96, no. 2, pp. 189鈥?98. CrossRef
  10. Herendi, T., Uniform Distribution of Linear Recurring Sequences modulo Prime Powers, / Finite Fields Appl., 2004, vol. 10, no. 1, pp. 1鈥?3. CrossRef
  11. Kuzmin, A.S. and Nechaev, A.A., A Generator of Uniform Pseudorandom Numbers, in / Veroyatnostnye metody v diskretnoi matematike (Probabilistic Methods in Discrete Mathematics, Abstr. 6th Int. Conf., Petrozavodsk, Russia, June 10鈥?6, 2004), Obozr. Prikl. Prom. Mat., 2004, vol. 11, pp. 969鈥?70.
  12. Kamlovskii, O.V., Distribution of / r-Tuples in One Class of Uniformly Distributed Sequences over Residue Rings, / Probl. Peredachi Inf., 2014, vol. 50, no. 1, pp. 98鈥?15 [ / Probl. Inf. Trans. (Engl. Transl.), 2014, vol. 50, no. 1, pp. 90鈥?05].
  13. Lahtonen, J., Ling, S., Sol茅, P., and Zinoviev, D., Z8-Kerdock Codes and Pseudorandom Binary Sequences, / J. Complexity, 2004, vol. 20, no. 2鈥?, pp. 318鈥?30. CrossRef
  14. Sol茅, P. and Zinoviev, D., The Most Significant Bit of Maximum-Length Sequences over Z 2 / _: Autocorrelation and Imbalance, / IEEE Trans. Inform. Theory, 2004, vol. 50, no. 8, pp. 1844鈥?846. CrossRef
  15. Sol茅, P. and Zinoviev, D., Distribution of / r-Patterns in the Most Significant Bit of a Maximum Length Sequence over Z 2 / _, / Proc. 3rd Int. Conf. on Sequences and Their Applications (SETA鈥?004), Seoul, Korea, Oct. 24鈥?8, 2004. Helleseth, T., Sarwate, D.V., Song, H.-Y., and Yang, K., Eds., Lect. Notes Comp. Sci, vol. 3486, Berlin: Springer, 2005, pp. 275鈥?81. CrossRef
  16. Sol茅, P. and Zinoviev, D., Galois Rings and Pseudo-Random Sequences, / Proc. 11th IMA Int. Conf. on Cryptography and Coding, Cirencester, UK, Dec. 18鈥?0, 2007, Galbraith, S.D., Ed., Lect. Notes Comp. Sci, vol. 4887, Berlin: Springer, 2007, pp. 16鈥?3.
  17. Fan, S. and Han, W., Random Properties of the Highest Level Sequences of Primitive Sequences over Z2 / e, / IEEE Trans. Inform. Theory, 2003, vol. 49, no. 6, pp. 1553鈥?557. CrossRef
  18. Kamlovskii, O.V., Exponential Sums Method for Frequencies of Most Significant Bit / r-Patterns in Linear Recurrent Sequences over Z2 / n, / Mat. Vopr. Kriptogr., 2010, vol. 1, no. 4, pp. 33鈥?2.
  19. Kamlovskii, O.V., Frequency Characteristics of Coordinate Sequences of Linear Recurrences over Galois Rings, / Izv. Ross. Akad. Nauk, Ser. Mat., 2013, vol. 77, no. 6, pp. 71鈥?6 [ / Izv. Math. (Engl. Transl.), 2013, vol. 77, no. 6, pp. 1130鈥?154]. CrossRef
  20. Solodovnikov, V.I., Bent Functions from a Finite Abelian Group to a Finite Abelian Group, / Diskret. Mat., 2002, vol. 14, no. 1, pp. 99鈥?13 [ / Discrete Math. Appl. (Engl. Transl.), 2002, vol. 12, no. 2, pp. 111鈥?26]. CrossRef
  21. Ambrosimov, A.S., Properties of Bent Functions of / q-Valued Logic over Finite Fields, / Diskret. Mat., 1994, vol. 6, no. 3, pp. 50鈥?0 [ / Discrete Math. Appl. (Engl. Transl.), 1994, vol. 4, no. 4, pp. 341鈥?50].
  
• 作者单位：O. V. Kamlovskii (1)
  
  1. Limited Liability Company 鈥淐ertification Test Center,鈥? Moscow, Russia
  
• ISSN：1608-3253

文摘

We consider the distribution of r-patterns in one class of uniformly distributed sequences over a finite field. We establish bounds for the number of occurrences of a given r-pattern and prove upper bounds for the cross-correlation function of these sequences.