Arithmetic crosscorrelations of feedback with carry shift register sequences

Abstract

Abstract-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) arithmetic crosscorrelations. These sequences are decimations of the 2-adic expansions of rational numbers p=q such that 2 is a primitive root modulo q.Index Terms-Crosscorrelations, binary sequences, feedback with carry shift register (FCSR) sequences, 2-adic numbers.

Fibonacci and Galois representations of feedback-with-carry shift registers

“…During the last few years, the feedback-with-carry shift register (FCSR) architectures and a simple modification, the -FCSR architectures have been investigated as alternative methods for the efficient generation of long pseudorandom binary sequences [1]- [3], [12], [14], [25]. The analysis of FCSR sequences has quite a different flavor from that of LFSR sequences, although they share an incredible list of parallel properties (see [7], [12], [13], [15], [16]). The FCSR circuits described in these papers resemble the "Fibonacci" configuration of the LSFR.…”

Explicit Bounds on Monomial and Binomial Exponential Sums

“…The theorem has a direct application to a conjecture of Goresky and Klapper [13] on the decimation of -sequences.…”

On the distinctness of modular reductions of maximal length sequences modulo odd prime powers

“…They are thought to be a source of ideal pseudorandom sequences (see [3], [4], [8], [17] and [18]). Through the exponential representation of FCSR sequences (see [8]), it can be found that, in fact, an FCSR sequence is the reduction modulo 2 of a linear recurring sequence of degree 1 over Z/(m) with odd positive integer m ≥ 3.…”