Results 11 to 20 of about 1,812,540 (189)
Some New Quantum BCH Codes over Finite Fields. [PDF]
Entropy (Basel), 2021 Quantum error correcting codes (QECCs) play an important role in preventing quantum information decoherence. Good quantum stabilizer codes were constructed by classical error correcting codes.
Xing L, Li Z.
europepmc +2 more sources
The Ring-LWE Problem in Lattice-Based Cryptography: The Case of Twisted Embeddings. [PDF]
Entropy (Basel), 2021 Several works have characterized weak instances of the Ring-LWE problem by exploring vulnerabilities arising from the use of algebraic structures. Although these weak instances are not addressed by worst-case hardness theorems, enabling other ring ...
Ortiz JN +4 more
europepmc +2 more sources
A Survey of Lattice-Based Physical-Layer Security for Wireless Systems with <i>p</i>-Modular Lattice Constructions. [PDF]
Entropy (Basel)Physical-layer security (PLS) provides an information-theoretic framework for securing wireless communications by exploiting channel and signal-structure asymmetries, thereby avoiding reliance on computational hardness assumptions.
Khodaiemehr H +5 more
europepmc +2 more sources
On Improperly Irregular Cyclotomic Fields. [PDF]
Proc Natl Acad Sci U S A, 1941 Not ...
Vandiver HS.
europepmc +4 more sources
CYCLOTOMIC POLYNOMIALS OVER CYCLOTOMIC FIELDS
Communications of the Korean Mathematical Society, 2012 In this paper, we find the minimal polynomial of a primitive root of unity over cyclotomic fields. From this, we factorize cyclotomic polynomials over cyclotomic fields and investigate the coefficients of when 3∤.
Sung-Doo Kim, June-Bok Lee
exaly +3 more sources
Cyclotomic orthomorphisms of finite fields
Discrete Applied Mathematics, 2013 AbstractIn this paper, we give explicit formulas for the number of cyclotomic orthomorphisms of Fq of index 3,4,5,6 for certain classes of prime powers q. We also give an explicit formula for the number of cyclotomic mappings of index 2 that are strong complete mappings of Fp for prime p.
exaly +2 more sources
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
doaj +1 more source
Unit Reducible Cyclotomic Fields [PDF]
, 2023 In this paper, we continue the study of unit reducible fields as introduced in \cite{LPL23} for the special case of cyclotomic fields. Specifically, we deduce that the cyclotomic fields of conductors $2,3,5,7,8,9,12,15$ are all unit reducible, and show ...
Leibak, Alar +3 more
core +1 more source
On the condition number of the Vandermonde matrix of the nth cyclotomic polynomial
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
doaj +1 more source
Constructions of Dense Lattices of Full Diversity
Trends in Computational and Applied Mathematics, 2020 A lattice construction using Z-submodules of rings of integers of number fields is presented. The construction yields rotated versions of the laminated lattices A_n for n = 2,3,4,5,6, which are the densest lattices in their respective dimensions.
A. A. Andrade +3 more
doaj +1 more source