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Feedback shift registers, 2-adic span, and combiners with memory
TLDR
This analysis gives a unified approach to the study of pseudorandom sequences, arithmetic codes, combiners with memory, and the Marsaglia-Zaman random number generator.
Fibonacci and Galois representations of feedback-with-carry shift registers
TLDR
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.
A new index for polytopes
TLDR
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.
2-Adic Shift Registers
TLDR
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.
An Introduction to Abstract Algebra
TLDR
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.
D-form Sequences: Families of Sequences with Low Correlation Values and Large Linear Spans
  • A. Klapper
  • Mathematics
    IEEE Trans. Inf. Theory
  • 1 March 1995
TLDR
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.
Arithmetic crosscorrelations of feedback with carry shift register sequences
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
Cross-correlations of geometric sequences in characteristic two
  • A. Klapper
  • Computer Science
    Des. Codes Cryptogr.
  • 1 October 1993
TLDR
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.
Arithmetic Cross-correlations of FCSR Sequences
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)
Cross-Correlations of Quadratic Form Sequences in Odd Characteristic
  • A. Klapper
  • Computer Science
    Des. Codes Cryptogr.
  • 1 July 1997
TLDR
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.
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