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Modified Cyclotomic Polynomial and Its Irreducibility
Mathematics, 2020 Finding irreducible polynomials over Q (or over Z ) is not always easy. However, it is well-known that the mth cyclotomic polynomials are irreducible over Q .
Ki-Suk Lee, Sung-Mo Yang, Soon-Mo Jung
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Cyclotomic Classes in a Product of Finite Abelian Groups and Applications
Journal of MathematicsCyclotomic classes of finite abelian groups have been extensively investigated for many decades, largely because of their nice algebraic structure and the breadth of their theoretical and practical applications.
Somphong Jitman
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On the condition number of the Vandermonde matrix of the nth cyclotomic polynomial [PDF]
Journal of Mathematical Cryptology, 2020 Recently, Blanco-Chacón proved the equivalence between the Ring Learning With Errors and Polynomial Learning With Errors problems for some families of cyclotomic number fields by giving some upper bounds for the condition number Cond(Vn) of the ...
Scala Antonio J. Di +2 more
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Research on Linear Complexity of Quaternary Sequences with Period 2pq [PDF]
Jisuanji gongcheng, 2016 Linear complexity is an important index for measuring the randomness properties of the sequences.Based on the theory of generalized cyclotomic,a new class of quaternary balanced generalized cyclotomic sequences with period 2pq over finite field F4 is ...
WEI Wanyin,DU Xiaoni,WANG Guohui
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A topological interpretation of the cyclotomic polynomial [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 We interpret the coefficients of the cyclotomic polynomial in terms of simplicial homology.
Gregg Musiker, Victor Reiner
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Mathematics, 2021 Linear complexity is an important property to measure the unpredictability of pseudo-random sequences. Trace representation is helpful for analyzing cryptography properties of pseudo-random sequences.
Jiang Ma +4 more
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Autocorrelation and Linear Complexity of Binary Generalized Cyclotomic Sequences with Period pq
Journal of Mathematics, 2021 Ding constructed a new cyclotomic class V0 ,V1. Based on it, a construction of generalized cyclotomic binary sequences with period pq is described, and their autocorrelation value, linear complexity, and minimal polynomial are confirmed.
Yan Wang +3 more
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Construction of Complex Lattice Codes via Cyclotomic Fields
Trends in Computational and Applied Mathematics, 2022 Through algebraic number theory and Construction $A$ we extend an algebraic procedure which generates complex lattice codes from the polynomial ring \mathbb{F}_{2}[x]/(x^{n}-1), where \mathbb{F}_{2}=\{0,1\}, by using ideals from the generalized ...
E. D. Carvalho +3 more
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Congruences from $q$-Catalan Identities [PDF]
Transactions on Combinatorics, 2016 In this paper, by studying three $q$-Catalan identities given by Andrews, we arrive at a certain number of congruences. These congruences are all modulo $Phi_n(q)$, the $n$-th cyclotomic polynomial or the related functions and modulo $q$-integers
Qing Zou
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Improved Ring LWR-Based Key Encapsulation Mechanism Using Cyclotomic Trinomials
IEEE Access, 2020 In the field of post-quantum cryptography, lattice-based cryptography has received the most noticeable attention. Most lattice-based cryptographic schemes are constructed based on the polynomial ring Rq = Zq[x]/f (x), using a cyclotomic polynomial f (x).
So Hyun Park +3 more
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