Abstract
We determine the linear complexity of p 2-periodic binary threshold sequences derived from polynomial quotient, which is defined by the function \((u^w-u^{wp})/p \pmod p\). When w = (p − 1)/2 and \(2^{p-1}\not\equiv 1 \pmod{p^2}\), we show that the linear complexity is equal to one of the following values \(\left\{p^2-1,\ p^2-p,\ (p^2+p)/2+1,\ (p^2-p)/2\right \}\), depending whether \(p\equiv 1,\ -1,\ 3,\ -3\pmod 8\). But it seems that the method can’t be applied to the case of general w.
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Chen, Z., Gómez-Pérez, D. (2012). Linear Complexity of Binary Sequences Derived from Polynomial Quotients. In: Helleseth, T., Jedwab, J. (eds) Sequences and Their Applications – SETA 2012. SETA 2012. Lecture Notes in Computer Science, vol 7280. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30615-0_17
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DOI: https://doi.org/10.1007/978-3-642-30615-0_17
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