Abstract
Binary and quaternary sequences with perfect periodic autocorrelation, and perfect nonlinear p m-ary sequences, are both shown to equate to orthogonal coboundaries — the simplest class of orthogonal cocycles. We consider doubly-indexed sequences defined by cocycles. We give a new construction — a generalised multiplication — of orthogonal cocycles and show it gives perfect nonlinear sequences for parameters where 1-dimensional PN sequences cannot exist.
This work was supported by Australian Research Council Grant A49701206.
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Horadam, K.J. (1999). Sequences from Cocycles. In: Fossorier, M., Imai, H., Lin, S., Poli, A. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1999. Lecture Notes in Computer Science, vol 1719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46796-3_12
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DOI: https://doi.org/10.1007/3-540-46796-3_12
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