Results 1 to 10 of about 64 (40)

A Construction of Optimal One-Coincidence Frequency-Hopping Sequences via Generalized Cyclotomy [PDF]

Entropy
Frequency-hopping sequences (FHSs) with low Hamming correlation are essential for synchronization and multiple-access communication systems. In this paper, we propose a novel construction of FHSs using generalized cyclotomy.
Minfeng Shao, Ying Miao
doaj   +6 more sources

New Generalized Cyclotomy and Its Applications

Finite Fields and Their Applications, 1998
Let \(n\geq 2\) be a positive integer and \(D_0\) a multiplicative subgroup of \(\mathbb{Z}^*_n\) (integer \(\text{mod }n\), coprime to \(n\)) of index \(d\). Let \(D_j= g_jD_0\), \(j= 1,2,\dots, d-1\). We call \(D_j\) the generalized cyclotomic classes of order \(d\) when \(n\) is composite and the classical cyclotomic classes of order \(d\) when \(n\)
Tor Helleseth
exaly   +3 more sources

On a Generalization of a Jacobi Exponential Sum Associated with Cyclotomy. [PDF]

Proc Natl Acad Sci U S A, 1950
Vandiver HS.
europepmc   +5 more sources

Linear Complexity and Trace Representation of New Ding Generalized Cyclotomic Sequences with Period pq and Order Two

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, Wei Zhao, Yanguo Jia, Xiumin Shen, Haiyang Jiang   +4 more
doaj   +1 more source

Frequency-Hopping Sequences With Optimal Average Hamming Correlation and Their Applications in Energy and Spectrum Harvesting Technologies Area

IEEE Access, 2021
The research of cyclotomy theory can be traced to Gauss and it has been applied to many fields such as cryptography, coding theory, and combinatorics. According to $v$ prime numbers or compound words, the incision on the residue-like ring ${\mathbb Z ...
Mingyue Fan
doaj   +1 more source

Cyclic Codes via the General Two-Prime Generalized Cyclotomic Sequence of Order Two

Journal of Mathematics, 2020
Suppose that p and q are two distinct odd prime numbers with n=pq. In this paper, the uniform representation of general two-prime generalized cyclotomy with order two over ℤn was demonstrated. Based on this general generalized cyclotomy, a type of binary
Xia Zhou
doaj   +1 more source

Linear Complexity of a New Class of Quaternary Generalized Cyclotomic Sequence with Period 2pm

Complexity, 2020
Sequences with high linear complexity property are of importance in applications. In this paper, based on the theory of generalized cyclotomy, new classes of quaternary generalized cyclotomic sequences with order 4 and period 2pm are constructed.
Pinhui Ke, Yan Zhong, Shengyuan Zhang
doaj   +1 more source

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

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

Generalizations of Partial Difference Sets from Cyclotomy to Nonelementary Abelian $p$-Groups [PDF]

The Electronic Journal of Combinatorics, 2008
A partial difference set having parameters $(n^2, r(n-1), n+r^2-3r,r^2-r)$ is called a Latin square type partial difference set, while a partial difference set having parameters $(n^2, r(n+1), -n+r^2+3r,r^2+r)$ is called a negative Latin square type partial difference set.
openaire   +3 more sources