$k$ -Fold Cyclotomy and Its Application to Frequency-Hopping Sequences

  title={\$k\$ -Fold Cyclotomy and Its Application to Frequency-Hopping Sequences},
  author={Jin-Ho Chung and Kyeongcheol Yang},
  journal={IEEE Transactions on Information Theory},
For an integer k ≥ 1, let , 1≤ qi ≤ k,be prime powers such that qi - Mif + 1 for some integers Mi and f. In this paper, the k-fold cyclotomy of Fqk × ⋯ × Fqk as a nontrivial generalization of the conventional cyclotomy (k = 1 case) and its application to frequency-hopping sequences (FHSs) are presented, where Fq 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… CONTINUE READING
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