New Generalized Cyclotomy and Its Applications

In this paper we first introduce a new generalized cyclotomy of order 2 with respect tope11•••pett, then we calculate the new cyclotomic numbers of order 2. Some applications of the new cyclotomy in sequences, cryptography, and coding theory are also discussed. In the last section of this paper, we introduce more generalized cyclotomies and point out their applications. The major motivation behind the new generalized cyclotomies is the construction of binary duadic codes.