Abstract
A Galois ring may be considered as a common generalization of a finite field and a prime power integer residue ring. The generalized Reed-Muller codes over finite fields were introduced by Kasami et al. and the generalized Reed-Muller codes over prime power integer residue rings were constructed by M. Bhaintwal and S. K. Wasan. In this paper, we give an unifying approach for these constructions.
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