Abstract
In this paper, for positive integers m, M, and a prime p such that M|p m – 1, we derive linear complexity over the prime field F p of M-ary Sidel’nikov sequences of period p m – 1 using discrete Fourier transform. As a special case, the linear complexity of the ternary Sidel’nikov sequence is presented. It turns out that the linear complexity of a ternary Sidel’nikov sequence with the symbol k 0 ≠1 at the (p m –1)/2-th position is nearly close to the period of the sequence, while that with k 0 =1 shows much lower value.
This research was supported by the MIC, Korea, under the ITRC support program and by the MOE, the MOCIE, and the MOLAB, Korea, through the fostering project of the Laboratory of Excellency.
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© 2006 Springer-Verlag Berlin Heidelberg
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Kim, YS., Chung, JS., No, JS., Chung, H. (2006). Linear Complexity over F p of Ternary 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_6
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DOI: https://doi.org/10.1007/11863854_6
Publisher Name: Springer, Berlin, Heidelberg
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