WebJun 4, 2024 · This paper contributes to constructing two classes of quantum synchronizable codes by the cyclotomic classes of order two over $\mathbb{Z}_{2q}$, whose synchronization capabilities can reach the upper bound under certain conditions. Moreover, the quantum synchronizable codes possess good error-correcting capability towards bit … WebCyclotomic definition, of or relating to cyclotomy. See more.
What do we know about the class group of cyclotomic fields over ...
In number theory, a cyclotomic field is a number field obtained by adjoining a complex root of unity to Q, the field of rational numbers. Cyclotomic fields played a crucial role in the development of modern algebra and number theory because of their relation with Fermat's Last Theorem. It was in the process of … See more For n ≥ 1, let ζn = e ∈ C; this is a primitive nth root of unity. Then the nth cyclotomic field is the extension Q(ζn) of Q generated by ζn. See more Gauss made early inroads in the theory of cyclotomic fields, in connection with the problem of constructing a regular n-gon with a compass and straightedge. His surprising result that had … See more (sequence A061653 in the OEIS), or OEIS: A055513 or OEIS: A000927 for the $${\displaystyle h}$$-part (for prime n) See more • Coates, John; Sujatha, R. (2006). Cyclotomic Fields and Zeta Values. Springer Monographs in Mathematics. Springer-Verlag See more • The nth cyclotomic polynomial • The conjugates of ζn in C are therefore the other primitive nth … See more A natural approach to proving Fermat's Last Theorem is to factor the binomial x + y , where n is an odd prime, appearing in one side of Fermat's equation $${\displaystyle x^{n}+y^{n}=z^{n}}$$ as follows: See more • Kronecker–Weber theorem • Cyclotomic polynomial See more Webthe class numbers of cyclotomic elds have only been determined for elds of small conductor, e.g. for prime conductors up to 67, due to the problem of nding the class number of its maximal real sub eld, a problem rst considered by Kummer. Our results have signi cantly improved the situation. litedb update many
Cyclotomic polynomial - Wikipedia
WebOct 1, 2024 · We derive the values of generating polynomials of cyclotomic classes of order 4, 6, 8 and consequently solve three problems pointed by Z. Dai et al. In fact, we study the discrete Fourier... WebOur Learn to Curl class is a one-hour instructor guided course to help teach the basic rules and fundamentals of Curling. This class is a prerequisite for new curlers before they can … WebMar 9, 2024 · By using the semiprimitive case of cyclotomic classes of order e, we show that {\mathcal {C}}_ {D} is a five-weight linear code and determine its weight distribution … imperial wilderness condo naples