Results 21 to 30 of about 160 (120)

Cyclotomy of Weil sums of binomials

Journal of Number Theory, 2015
The Weil sum $W_{K,d}(a)=\sum_{x \in K} ψ(x^d + a x)$ where $K$ is a finite field, $ψ$ is an additive character of $K$, $d$ is coprime to $|K^\times|$, and $a \in K^\times$ arises often in number-theoretic calculations, and in applications to finite geometry, cryptography, digital sequence design, and coding theory.
Yves Aubry, Daniel J. Katz, Philippe Langevin   +2 more
openaire   +2 more sources

New class of frequency-hopping sequences set with optimal average Hamming correlation property

Tongxin xuebao, 2012
The average Hamming correlation is an important performance parameter of frequency-hopping sequences.A generalization of Whiteman cyclotomy was proposed and then some properties of the new defined cyclotomy classes were presented.Based on the ...
Pin-hui KE, Hai-hui ZHANG, Sheng-yuan ZHANG   +2 more
doaj   +2 more sources

On the Linear Complexity of New Generalized Cyclotomic Binary Sequences of Order Two and Period pqr

Tsinghua Science and Technology, 2016
Periodic sequences over finite fields, constructed by classical cyclotomic classes and generalized cyclotomic classes, have good pseudorandom properties.
Longfei Liu, Xiaoyuan Yang, Xiaoni Du, Bin Wei   +3 more
doaj   +1 more source

Cyclotomy and addition sets

Journal of Combinatorial Theory, Series A, 1977
\(A(v,k,\lambda,g)\) - addition set \(A=(a_1,\dots,a_k)\) is a collection of \(k\) distinct residues modulo \(v\) such that any non-zero residue \(\gamma\) has exactly \(\lambda\) representations of the form \(a_i+ga_j\equiv\gamma\). If the polynomial \(\theta(x)=x^{a_1}+\dots+x^{a_k}\) is considered this leads to \(\theta(x)\theta(x^g)\equiv d+\lambda(
openaire   +2 more sources

Cycle Structure and Adjacency Graphs of a Class of LFSRs and a New Family of De Bruijn Cycles

IEEE Access, 2018
Feedback shift registers can be applied to the fields of communications, stream ciphers, computers, and design theory. The linear feedback shift registers are often used in the construction of De Bruijn sequences. For any given linear shift register, its
Xiaofang Wang, Linzhi Jiang
doaj   +1 more source

Autocorrelation Values of Generalized Cyclotomic Sequences with Period pⁿ⁺¹

Mathematics, 2019
Recently Edemskiy proposed a method for computing the linear complexity of generalized cyclotomic binary sequences of period p n + 1 , where p = d R + 1 is an odd prime, d , R are two non-negative integers, and n > 0 ...
Xiaolin Chen, Huaning Liu
doaj   +1 more source

Genuinely nonabelian partial difference sets

Journal of Combinatorial Designs, Volume 32, Issue 7, Page 351-370, July 2024.
Abstract Strongly regular graphs (SRGs) provide a fertile area of exploration in algebraic combinatorics, integrating techniques in graph theory, linear algebra, group theory, finite fields, finite geometry, and number theory. Of particular interest are those SRGs with a large automorphism group.
John Polhill, James A. Davis, Ken W. Smith, Eric Swartz   +3 more
wiley   +1 more source

New constructions for disjoint partial difference families and external partial difference families

Journal of Combinatorial Designs, Volume 32, Issue 4, Page 190-213, April 2024.
Abstract Recently, new combinatorial structures called disjoint partial difference families (DPDFs) and external partial difference families (EPDFs) were introduced, which simultaneously generalize partial difference sets, disjoint difference families and external difference families, and have applications in information security.
Sophie Huczynska, Laura Johnson
wiley   +1 more source

Beyond uniform cyclotomy

Finite Fields and Their Applications
Cyclotomy, the study of cyclotomic classes and cyclotomic numbers, is an area of number theory first studied by Gauss. It has natural applications in discrete mathematics and information theory. Despite this long history, there are significant limitations to what is known explicitly about cyclotomic numbers, which limits the use of cyclotomy in ...
Sophie Huczynska, Laura M. Johnson, Maura B. Paterson   +2 more
openaire   +6 more sources

Cyclotomy with short periods [PDF]

Mathematics of Computation, 1983
This paper develops cyclotomy for periods of lengths 2, 3 and 4 for moduli which are primes and products of two primes.
Lehmer, D. H., Lehmer, Emma
openaire   +1 more source