Negacyclic codes of length 2/sup s/ over galois rings

Codes over the ring of integers modulo 4 have been studied by many researchers. Negacyclic codes such that the length n of the code is odd have been characterized over the alphabet Zopf
₄
, and furthermore, have been generalized to the case of the alphabet being a finite commutative chain ring. In this paper, we investigate negacyclic codes of length 2
^s
over Galois rings. The structure of negacyclic codes of length 2
^s
over the Galois rings GR(2
^a
,m), as well as that of their duals, are completely obtained. The Hamming distances of negacyclic codes over GR(2
^a
,m) in general, and over Zopf
₂

^a
in particular are studied. Among other more general results, the Hamming distances of all negacyclic codes over Zopf
₂

^a
of length 4,8, and 16 are given. The weight distributions of such negacyclic codes are also discussed