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The Adjacency Graphs of Linear Feedback Shift Registers with Primitive-like Characteristic Polynomials
feedback shift register adjacency graph De Bruijn sequence
2016/3/11
We consider the adjacency graphs of the linear feedback shift registers (LFSRs) with characteristic polynomials of the form l(x)p(x), where l(x) is a polynomial of small degree and p(x) is a primitive...
SPLITTING FIELDS OF CHARACTERISTIC POLYNOMIALS OF RANDOM ELEMENTS IN ARITHMETIC GROUPS
SPLITTING FIELDS CHARACTERISTIC POLYNOMIALS RANDOM ELEMENTS ARITHMETIC GROUPS
2015/8/26
We discuss rather systematically the principle, implicit in earlier works, that for a “random” element in an arithmetic subgroup of a (split, say) reductive algebraic group over a number field, the sp...
Freezing Transition, Characteristic Polynomials of Random Matrices, and the Riemann Zeta-Function
Freezing Transition Characteristic Polynomials Random Matrices the Riemann Zeta-Function
2012/2/24
We argue that the freezing transition scenario, previously explored in the statistical mechanics of 1/f-noise random energy models, also determines the value distribution of the maximum of the modulus...
Average characteristic polynomials in the two-matrix model
Two-matrix model average characteristic polynomial
2010/12/6
The two-matrix model is defined on pairs of Hermitian matrices (M1,M2) of size n × n by the probability measure 1 Zn exp (Tr(−V (M1) −W(M2) + M1M2)) dM1 dM2, where V and W are given poten...
Correlations of RMT Characteristic Polynomials and Integrability: Hermitean Matrices
non-Gaussian ensembles Hermitean random matrices tau-functions
2010/4/6
Integrable theory is formulated for correlation functions of characteristic polynomials associated with invariant non-Gaussian ensembles of Hermitean random matrices. By embedding the correlation func...
Finding Characteristic Polynomials with Jump Indices
MICKEY stream cipher ECRYPT irregular cloc
2008/10/20
Jansen introduced a technique for building LFSRs that can be clocked a large number of times with a single simple operation. These may be useful in the construction of stream ciphers based on clock-co...