Results 1 to 10 of about 101 (69)

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.
Ying Miao, Minfeng Shao
exaly   +4 more sources

Finite Fourier Series and Cyclotomy [PDF]

Proceedings of the National Academy of Sciences of the United States of America, 1951
Whiteman AL.
exaly   +2 more sources

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

Proceedings of the National Academy of Sciences of the United States of America, 1950
H S Vandiver
exaly   +2 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

On Some New Almost Difference Sets Constructed from Cyclotomic Classes of Order 12

Recoletos Multidisciplinary Research Journal, 2023
Almost Difference Sets have extensive applications in coding theory and cryptography. In this study, we introduce new constructions of Almost Difference Sets derived from cyclotomic classes of order 12 in the finite field GF(q), where q is a prime ...
Benedict Estrella
doaj   +1 more source

Optimal Constructions of Low-Hit-Zone Frequency-Hopping Sequence Sets via Cyclotomy

IEEE Access, 2023
In complex environments of wireless communication, to improve the communication anti-interference performance, quasi-synchronous frequency-hopping (FH) communication system requires low-hit-zone (LHZ) FH sequence sets with optimal Hamming correlation (HC)
Changyuan Wang, Yi Zhang, Kanglin Wei, Qin Yu, Fuyou Fan   +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

Almost Difference Set Pairs and Ideal Three-Level Correlation Binary Sequence Pairs

IEEE Access, 2020
Almost difference set pairs are used in cryptography and coding theory, and a majority of the acknowledged almost difference set pairs are constructed by Chinese remainder theorem, cyclotomy or interleaving.
Wei Zhao, Yue Wu, Yaya Zhang, Yanguo Jia
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