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Linear complexity of Legendre-polynomial quotients

Linear complexity of Legendre-polynomial quotients

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Let p be an odd prime and be a positive integer. The authors continue to investigate the binary sequence over defined from polynomial quotients by modulo p. The is generated in terms of which equals to the Legendre symbol of for u ≥ 0. In an earlier work, the linear complexity of was determined for (i.e. the case of Fermat quotients) under the assumption of . In this work, they develop a naive trick to calculate all possible values on the linear complexity of for all under the same assumption. They also state that the case of larger can be reduced to that of . So far, the linear complexity is almost determined for all kinds of Legendre-polynomial quotients.

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