This analysis gives a unified approach to the study of pseudorandom sequences, arithmetic codes, combiners with memory, and the Marsaglia-Zaman random number generator.Expand

The d-FCSR, a slight modification of the (Fibonacci) FCSR architecture in which the feedback bit is delayed for d clock cycles before being returned to the first cell of the shift register, admits a more efficient "Galois" architecture.Expand

A new index for convex polytopes is introduced, a vector whose length is the dimension of the linear span of the flag vectors of poly topes, equivalent to the generalized Dehn-Sommerville equations.Expand

An algebraic framework is described, based on algebra over the 2-adic numbers, in which the sequences generated by FCSRs can be analyzed, in much the same way that algebra over finite fields can be used to analyze LFSR sequences.Expand

This chapter describes a variety of basic algebraic structures that play roles in the generation and analysis of sequences, especially sequences intended for use in communications and cryptography.Expand

The author describes a method for constructing large families of binary sequences from families of homogeneous functions over finite fields, satisfying certain properties and uses this general method to construct specific families of sequences with optimal correlations and exponentially better linear span than No sequences.Expand

An arithmetic version of the crosscorrelation of two sequences is defined, generalizing Mandelbaum's (1967) arithmetic autocorrelations. Large families of sequences are constructed with ideal… Expand

Cross-correlation functions are determined for a large class of geometric sequences based on m-sequences in characteristic two, showing that geometric sequences are candidates for use in spread-spectrum communications systems in which cryptographic security is a factor.Expand

An arithmetic version of the crosscorrelation of two sequences is defined, generalizing Mandelbaum’s arithmetic autocorrelations. Large families of sequences are constructed with ideal (vanishing)… Expand

Cross-correlation functions are determined for a large class of geometric sequences based on m-sequences in odd characteristic, showing that geometric sequences are candidates for use in spread-spectrum communications systems in which cryptographic security is a factor.Expand