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

Abstract

In this paper, we introduce a vectorial conception of d-FC-SRs 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.