The Gray Image of Codes over Finite Chain Rings

The results of J. F. Qian et al. [5] on (1 − γ)-constacyclic codes over finite chain rings of nilpotency index 2 are extended to (1 − γe)constacyclic codes over finite chain rings of arbitrary nilpotency index e+1. The Gray map is introduced for this type of rings. We prove that the Gray image of a linear (1− γe)-constacyclic code over a finite chain ring is a distance-invariant quasi-cyclic code over its residue field. When the length of codes and the characteristic of a ring are relatively prime, the Gray images of a linear cyclic code and a linear (1+γe)-constacyclic code are permutatively to quasi-cyclic codes over its residue field. Mathematics Subject Classification: 94B15, 94B60, 94B99