k-Fold Cyclotomy and Its Application to Frequency-Hopping Sequences
SCIE
SCOPUS
- Title
- k-Fold Cyclotomy and Its Application to Frequency-Hopping Sequences
- Authors
- Chung, JH; Yang, K
- Date Issued
- 2011-04
- Publisher
- IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
- Abstract
- For an integer, k >= 1, let q(i), 1 <= i <= k, be prime powers such that q(i) = M-i f + 1 for some integers M-i and f. In this paper, the k-fold cyclotomy of proves (q1) X center dot center dot center dot X proves q(k) as a nontrivial generalization of the conventional cyclotomy (k = 1 case) and its application to frequency-hopping sequences (FHSs) are presented, where F-q is the finite field with q elements. First, the definitions of k-fold cyclotomic classes and k-fold cyclotomic numbers are given. And then, their basic properties including k-fold diagonal sums are derived. Based on them, new optimal FHS sets of length N and frequency set size M or M + 1 with respect to the Peng-Fan bound are constructed for a product N of distinct odd primes and a divisor M of N - 1. Furthermore, new optimal FHSs of length N and frequency set size M with respect to the Lempel-Greenberger bound are constructed when N has at least one prime factor which is 3 modulo 4 and (N -1)/M is an even integer. Our constructions give several new optimal parameters not covered in the literature, which are summarized in Table I.
- Keywords
- Cyclotomic numbers; frequency-hopping sequences; generalized cyclotomy; Hamming correlation; power-residue sequences; BOUNDS; CODES; SETS
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/17559
- DOI
- 10.1109/TIT.2011.2112235
- ISSN
- 0018-9448
- Article Type
- Article
- Citation
- IEEE TRANSACTIONS ON INFORMATION THEORY, vol. 57, no. 4, page. 2306 - 2317, 2011-04
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