Vectorial FCSR constructed on totally ramified extension of the p-adic numbers

Abdelaziz Marjane

In this paper, we introduce a vectorial conception of d-FCSRs to build these registers over any finite field. We describe the structure of d-vectorial FCSRs and we develop an analysis to obtain basic properties like periodicity and the existence of maximal length sequences. To illustrate these vectorial d-FCSRs, we present simple examples and we compare with those of Goresky, Klapper and Xu. Keywords: LFSR, FCSR, vectorial FCSR, d-FCSR, sequences, periodicity, p-adic, ?-adic, maximal period.

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