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arXiv · 1306.5648

Trace representation and linear complexity of binary sequences derived from Fermat quotients

Zhixiong Chen
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Abstract

We describe the trace representations of two families of binary sequences derived from Fermat quotients modulo an odd prime $p$ (one is the binary threshold sequences, the other is the Legendre-Fermat quotient sequences) via determining the defining pairs of all binary characteristic sequences of cosets, which coincide with the sets of pre-images modulo $p^2$ of each fixed value of Fermat quotients. From the defining pairs, we can obtain an earlier result of linear complexity for the binary threshold sequences and a new result of linear complexity for the Legendre-Fermat quotient sequences under the assumption of $2^{p-1}\not\equiv 1 \bmod {p^2}$.

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Zhixiong Chen. 2013-06-20. Trace representation and linear complexity of binary sequences derived from Fermat quotients. https://doi.org/10.1007/s11432-014-5092-x

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