On the linear complexity of generalized cyclotomic sequences with the period \(p^m\). (English) Zbl 1234.94025
Summary: This letter contributes to the investigation of the linear complexity of generalized cyclotomic sequences with the period \(p^m\), which are contained by the sequences constructed by C. Ding and T. Helleseth in 1998 [Finite Fields Appl. 4, No. 2, 140–166 (1998; Zbl 0908.11058)], as a representative special case. The results obtained confirm that all of these sequences have high linear complexity.
MSC:
| 94A55 | Shift register sequences and sequences over finite alphabets in information and communication theory |
| 11T71 | Algebraic coding theory; cryptography (number-theoretic aspects) |
| 68Q25 | Analysis of algorithms and problem complexity |
| 94A60 | Cryptography |
Citations:
Zbl 0908.11058References:
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| [2] | Bai, E.; Liu, X.; Xiao, G., Linear complexity of new generalized cyclotomic sequences of order two of length \(p q\), IEEE Trans. Inform. Theory, 51, 5, 1849-1854 (2005) · Zbl 1234.94019 |
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| [4] | Cusick, T.; Ding, C.; Renvall, A., Stream Ciphers and Number Theory, (North-Holland Mathematical Library, vol. 66 (1998), Elsevier Science Pub. Co) · Zbl 0930.11086 |
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| [7] | Ding, C.; Helleseth, T., New generalized cyclotomy and its applications, Finite Fields Appl., 4, 140-166 (1998) · Zbl 0908.11058 |
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