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Periodicity and Correlation Properties of dFCSR Sequences
, 2001
"... Abstract. A dfeedbackwithcarry shift register (dFCSR) is a finite state machine, similar to a linear feedback shift register (LFSR), in which a small amount of memory and a delay (by dclock cycles) is used in the feedback algorithm (see Goresky and Klapper [4,5]). The output sequences of these ..."
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Abstract. A dfeedbackwithcarry shift register (dFCSR) is a finite state machine, similar to a linear feedback shift register (LFSR), in which a small amount of memory and a delay (by dclock cycles) is used in the feedback algorithm (see Goresky and Klapper [4,5]). The output sequences of these simple devices may be described using arithmetic in a ramified extension field of the rational numbers. In this paper we show how many of these sequences may also be described using simple integer arithmetic, and consequently how to find such sequences with large periods. We also analyze the ‘‘arithmetic crosscorrelation’’ between pairs of these sequences and show that it often vanishes identically.
A New Class of Pseudonoise Sequences
, 2003
"... We apply the framework of adic algebra and algebraic feedback shift registers to polynomial rings over nite elds. We give a construction of new pseudorandom sequences over a nonprime nite eld that satisfy Golomb's randomness criteria. ..."
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We apply the framework of adic algebra and algebraic feedback shift registers to polynomial rings over nite elds. We give a construction of new pseudorandom sequences over a nonprime nite eld that satisfy Golomb's randomness criteria.