An arithmetic or with-carry analog of Blahut’s theorem is presented. This relates the length of the smallest feedback with carry shift register to the number of nonzero classical Fourier coefficients of a periodic binary sequence.

Using the structure of Singer cycles in general linear groups, we prove that a conjecture of Zeng, Han and He (2007) holds in the affirmative in a special case, and outline a plausible approach to prove it in the general case. This conjecture is about the number of primitive σ-LFSRs of a given order over a finite field, and it generalizes a known formula for the number of primitive LFSRs, which...

Shift work exerts major influences on the physiological functions of the human body. These are primarily mediated by the disruption of circadian rhythms since most body functions are circadian rhythmic. Next to the disturbances caused by changes in the circadian system, shift work has also been suggested to be related to a number of other health disorders. The present study summarizes recently ...

Let s = (s 1 ; s 2 ; : : : ; s n) be a sequence of characters where s i 2 Z p for 1 i n. One measure of the complexity of the sequence s is the length of the shortest feedback shift register that will generate s, which is known as the maximum order complexity of s 17, 18]. We provide a proof that the expected length of the shortest feedback register to generate a sequence of length n is less th...

Economics education needs a paradigm shift given the failure of traditional models to address root causes systemic injustice accurately and humanely. After summarizing some existing research that critiques economic practices offers new paradigms for teachers students consider, three orientations are offered. Economic should start with students, build from bottom up, critique official knowledge.

A new fault coverage test pattern generator using a linear feedback shift register (LFSR) called FC-LFSR can perform fault analysis and reduce the power of a circuit during test by generating three intermediate patterns between the random patterns by reducing the hardware utilization. The goal of having intermediate patterns is to reduce the transitional activities of Primary Inputs (PI) which ...

In this paper, feedback with carry shift registers (FCSRs) are analyzed with main focus on the general case of FCSRs with arbitrary connection integer and on maximum-period FCSRs. Moreover, a keystream generator that employs the structure of the linear feedback shift register (LFSR)-based Geffegenerator is studied in connection with FCSRs as a special nonlinear combining generator. The consider...