The minimal polynomial of 2cos(π/q) and Dickson polynomials

2012 ◽  
Vol 218 (13) ◽  
pp. 7014-7022 ◽  
Author(s):  
Abdelmejid Bayad ◽  
Ismail Naci Cangul
Keyword(s):  
Minimal Polynomial ◽  
Dickson Polynomials

scholarly journals DIOPHANTINE SETS OF POLYNOMIALS OVER ALGEBRAIC EXTENSIONS OF THE RATIONALS

2014 ◽  
Vol 79 (3) ◽  
pp. 733-747
Author(s):  
CLAUDIA DEGROOTE ◽  
JEROEN DEMEYER
Keyword(s):  
Minimal Polynomial ◽  
Finite Extension ◽  
Algebraic Extension ◽  
Recursively Enumerable

AbstractLet L be a recursive algebraic extension of ℚ. Assume that, given α ∈ L, we can compute the roots in L of its minimal polynomial over ℚ and we can determine which roots are Aut(L)-conjugate to α. We prove that there exists a pair of polynomials that characterizes the Aut(L)-conjugates of α, and that these polynomials can be effectively computed. Assume furthermore that L can be embedded in ℝ, or in a finite extension of ℚp (with p an odd prime). Then we show that subsets of L[X]k that are recursively enumerable for every recursive presentation of L[X], are diophantine over L[X].

An extension of the Cobham-Semënov Theorem

2000 ◽  
Vol 65 (1) ◽  
pp. 201-211 ◽  
Author(s):  
Alexis Bès
Keyword(s):  
Characteristic Polynomial ◽  
Minimal Polynomial ◽  
Pisot Numbers ◽  
Numeration Systems

AbstractLet θ, θ′ be two multiplicatively independent Pisot numbers, and letU,U′ be two linear numeration systems whose characteristic polynomial is the minimal polynomial of θ and θ′, respectively. For everyn≥ 1, ifA⊆ ℕnisU-andU′ -recognizable thenAis definable in 〈ℕ: + 〉.

On the degree of the minimal polynomial of the Lyapunov operator

1974 ◽  
Vol 78 (3) ◽  
pp. 229-236 ◽  
Author(s):  
Marvin Marcus ◽  
M. Shafqat Ali
Keyword(s):  
Minimal Polynomial ◽  
Lyapunov Operator

scholarly journals Autocorrelation and Linear Complexity of Binary Generalized Cyclotomic Sequences with Period pq

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Yan Wang ◽  
Liantao Yan ◽  
Qing Tian ◽  
Liping Ding
Keyword(s):  
Autocorrelation Function ◽  
Linear Complexity ◽  
Minimal Polynomial ◽  
Binary Sequences ◽  
Cyclotomic Class ◽  
Cyclotomic Sequences ◽  
Autocorrelation Value

Ding constructed a new cyclotomic class V 0   , V 1 . Based on it, a construction of generalized cyclotomic binary sequences with period p q is described, and their autocorrelation value, linear complexity, and minimal polynomial are confirmed. The autocorrelation function C S w is 3-level if p ≡ 3 mod 4 , and C S w is 5-level if p ≡ 1 mod 4 . The linear complexity LC S > p q / 2 if p ≡ 1   mod   8 , p > q + 1 , or p ≡ 3 mod 4 or p ≡ − 3 mod 8 . The results show that these sequences have quite good cryptographic properties in the aspect of autocorrelation and linear complexity.

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