Summary
Binary sequences of period n = p m − 1 for an odd prime p are introduced in [4] by taking the characteristic sequence of the image set of the polynomial (z + 1)d +az d + b over the finite field \({{F}_{{{{p}^{m}}}}}\) of p m elements. It was shown in [4] that they are (almost) balanced and have optimal autocorrelation in the case where the polynomial can be transformed into the form z 2 − c. In this paper, we show that the sequences are (almost) balanced and have optimal autocorrelation in the case of \(d = ({{p}^{m}} + 1)/2, a = {{( - 1)}^{{d - 1}}}\) and b = ±1. Furthermore, we show that they are equivalent to the Lempel-Cohn-Eastman sequence in [2] in the balanced case. We also give a direct proof of the autocorrelation property of the Lempel-Cohn- Eastman sequence and discuss its linear complexity.
*This work was supported in part by the Norwegian Research Council and by the BK21 Program of the Ministry of Education of Korea and the Com2Mac of Postech.
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© 2002 Springer-Verlag London
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Helleseth, T., Yang, K. (2002). On Binary Sequences of Period n = pm ∓ 1 with Optimal Autocorrelation. In: Helleseth, T., Kumar, P.V., Yang, K. (eds) Sequences and their Applications. Discrete Mathematics and Theoretical Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-0673-9_15
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DOI: https://doi.org/10.1007/978-1-4471-0673-9_15
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