Abstract
In this paper we derive a lower bound on the linear complexity and an upper bound on the 1-error linear complexity over F p of M-ary Sidel’nikov sequences of period p m–1 when M≥3 and p≡±1 mod M. In particular, we exactly compute the 1-error linear complexity of ternary Sidel’nikov sequences when p≡–1 mod 3 and m≥4. Furthermore, we give a tighter lower bound on the linear complexity of ternary and quaternary Sidel’nikov sequences for p≡–1 mod M by a more detailed analysis. Based on these results, we present the ratios of the linear complexity and the 1-error linear complexity to the period asymptotically.
This work was supported by grant No. R01-2003-000-10330-0 from the Basic Research Program of the Korea Science and Engineering Foundation.
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Chung, JH., Yang, K. (2006). Bounds on the Linear Complexity and the 1-Error Linear Complexity over F p of M-ary Sidel’nikov Sequences. In: Gong, G., Helleseth, T., Song, HY., Yang, K. (eds) Sequences and Their Applications – SETA 2006. SETA 2006. Lecture Notes in Computer Science, vol 4086. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11863854_7
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DOI: https://doi.org/10.1007/11863854_7
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