Vectorial Feedback with Carry Registers and Memory requirements

In \cite{marjane2010}, we have introduced vectorial conception of FCSR's in Fibonacci mode. This conception allows us to easily analyze FCSR's over binary finite fields $\mathbb{F}_{2^{n}}$ for $n\geq 2$. In \cite{allailou2010}, we describe and study the corresponding Galois mode and use it to design a new stream cipher. In this paper, we introduce the Ring mode for vectorial FCSR, explain the analysis of such Feedback registers and illustrate with a simple example.Comment: 12 pages, 4 figure

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

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.Comment: 18 pages, 8 figure