Cyclotomic classes

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August undefined, 2024

WebJan 3, 2012 · In this paper, we give a construction of strongly regular Cayley graphs and a construction of skew Hadamard difference sets. Both constructions are based on choosing cyclotomic classes in finite fields, and they generalize the constructions given by Feng and Xiang \\cite{FX111,FX113}. Three infinite families of strongly regular graphs with new … WebIn recent years, many classes of linear codes with interesting parameters have been obtained with this technique. Based on quadratic Gauss sums, the puncturing technique and cyclotomic classes, we investigate two classes of …

Cyclotomic field - 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... WebLeopoldt concentrated on a fixed cyclotomic field, and established various p-adic analogues of the classical complex analytic class number formulas. In particular, this led him to introduce, with Kubota, p-adic analogues of the complex L-functions attached to cyclotomic extensions of the rationals. phillips and solo 1992

On the Iwasawa invariants of prime cyclotomic fields - ResearchGate

Web20 hours ago · I defined the arithmetic operators for a S4 class cyclotomic: cyclotomic_arith_cyclotomic <- function(e1, e2) { switch( .Generic, "+" = sumCyc(e1, e2), "-" = su... WebFeb 15, 2002 · ldenotes the class group of the ring of integers of the real cyclotomic eld Q( l + 1 l). Its order, theclass numberof Q( l 1 l), is denoted byh l. The quotient groupCl lis rather well understood. Already in the 19th century, E.E. Kummer [12], [13] computed the orders of the groupsCl lforl<100. phillips and riley funeral montgomery al

Cyclotomy and arithmetic properties of some families in Z[x]/ …

Linear Complexity of A Class of Quaternary Sequences

WebDec 1, 1985 · In the first part of the paper we show how to construct real cyclotomic fields with large class numbers. If the GRH holds then the class number hp+ of the p th real … WebSep 9, 2024 · This study shows the construction of difference sets in the additive group of the field GF (q) from unions of cyclotomic classes of order N = 14 using a computer … phillip sandsWeb1. Cyclotomic ﬁelds 3 2. An outline of class ﬁeld theory 4 3. Relative class number formula and Stickelberger’s theorem 6 4. Basic properties of Gauss sum 7 5. Prime factorization of Gauss sum 10 6. A consequence of the Kummer–Vandiver conjecture 14 7. Kummer theory 16 8. Cyclicity theorem for F0 = Q[µp] 17 9. Proof of the cyclicity ... phillips and simmonds 2013

"WebBy virtue of the cyclotomic numbers of orders two and four, we determine the values of ( i, j, k) 2 for i, j, k ∈ { 0, 1 }, which may be of independent interest. As an application, we give another proof of the c -differential spectrum of an AP c N function over finite fields with characteristic 5. " - Cyclotomic classes

Cyclotomic classes

[1201.0701] Constructions of Strongly Regular Cayley Graphs and …

WebNov 1, 2016 · In this paper, 2-adic complexity of two classes of generalized cyclotomic binary sequences is investigated. The sequences in the first class have period p (p+4), and their 2-adic complexity attains ... View via Publisher Save to Library Create Alert Cite 11 Citations Citation Type More Filters WebMar 26, 2024 · An important theorem that describes the structure of the class groups of cyclotomic fields in terms of $ p $-adic $ L $-functions has been proved by B. Mazur and A. Wiles (see [a1], [a4]) with the help of methods from algebraic geometry. References How to Cite This Entry: Cyclotomic field. Encyclopedia of Mathematics.

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WebJun 4, 2024 · This paper contributes to constructing two classes of quantum synchronizable codes by the cyclotomic classes of order two over , whose synchronization capabilities … 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 …

WebNov 25, 2016 · Kummer's class number formula gives for the first factor $ 37 $ and the second factor can be determined to $ 1 $ by the Minkowski bound in the real … WebLinear complexity is an important criterion to characterize the unpredictability of pseudo-random sequences, and large linear complexity corresponds to high cryptographic strength. Pseudo-random Sequences with a large linear complexity property are of importance in many domains. In this paper, based on the theory of inverse Gray mapping, two classes …

WebMar 26, 2024 · An important theorem that describes the structure of the class groups of cyclotomic fields in terms of $ p $-adic $ L $-functions has been proved by B. Mazur … WebFeb 17, 2024 · Classes follow local and CDC guidelines. Locations offer weekly classes as well as multi-sibling classes and private classes; offerings include baby swimming …

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 …

WebA partition of is a family of sets, satisfying If there exist a subgroup of and of , satisfying ,, then the are called to be classical cyclotomic classes with order if is a prime number, and generalized cyclotomic classes with order if is a composite number. The (generalized) cyclotomic numbers with order are defined as. Lemma 4. phillips and schmidt asheville ncWebthe 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. try the wine clockworkWebcyclotomic classes is described in Section 3. 2 DSS and quadratic residues Let D = {x 1, x 2,...,x k} be a (v,k,λ) diﬀerence set (cf. [1], [2], [7]), that is, a subset of k residues modulo v such that every positive residue modulo v occurs exactly λ times in the multi-set of diﬀerences {x i −x phillips and schmitt ddsWebn generate the group of cyclotomic units. If n is a composite number having two or more distinct prime factors, then ζ a n − 1 is a unit. The subgroup of cyclotomic units … phillips and sonsWebThere are many classes, camps, and enrichment programs that can help keep kids focused on STEAM — Science, Technology, Engineering, Art, and Math. Check out this reader … try the wine gifWebMay 14, 2024 · cyclotomic: [adjective] relating to, being, or containing a polynomial of the form xp−1 + xp−2 + … + x + 1 where p is a prime number. phillips and son livestock auction todayWeb6= 1, is the root of an irreducible (cyclotomic polynomial) polynomial of degree 4. Hence [K: Q] = 4. 1. 2 GREGG MUSIKER ... From class we saw that if f( ) = 0, then the automorphisms of Q( ) send to another root of f(x). This … trytheworld.com