k-fold cyclotomic numbers and their applications to frequency-hopping sequences
Jin-Ho Chung, Kyeongcheol Yang · 2010
For an integer k ≥ 1, k-fold cyclotomic numbers of Fq1× ... × Fqkare introduced, where Fqis the finite field with q elements and qi's are powers of distinct primes. They are a generalization of the conventional cyclotomic numbers (k = 1 case). Some of their basic properties including k-fold diagonal sums are derived. As an application of the k-fold cyclotomy, frequency-hopping sequences (FHSs) of length p1... pkare constructed for distinct odd primes p1, ..., pk, which are optimal with respect to the Lempel-Greenberger bound and the Peng-Fan bound.