Abstract

The q-orbits of the permutation μq of 1+rZnr, denoted by (1+rZnr)∕μq, are characterized by using Möbius inversion formula and the Generalized Chinese Remainder Theorem. Then the (−ph)-orbits of the permutation μ−ph of (1+rZnr)∕μq are characterized and enumerated. As applications, the explicit enumeration formulas for constacyclic codes concerned with ph-dualities are obtained, and several classes of ph-LCD MDS constacyclic codes are constructed. These characterizations are generalized to the q-cyclotomic cosets modulo (n1,…,nr) which find applications in studying abelian codes.

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