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Negacyclic Codes of Length 2^{s} Over Galois Rings

12/01/2005
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 ℤ4, 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 2s over Galois rings. The structure of negacyclic codes of length 2s over the Galois rings GR(2a, m), as well as that of their duals, are completely obtained. The Hamming distances of negacyclic codes over GR(2a, m) in general, and over ℤ2a in particular are studied. Among other more general results, the Hamming distances of all negacyclic codes over ℤ2a of length 4, 8, and 16 are given. The weight distributions of such negacyclic codes are also discussed.