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S.D. Berman gave in 1967 a formula of the minimal distance of the FG-codes (RadF G) i for i = 0,...,p m − 1, where G is a cyclic group of order p m , and F a finite field with characteristic p. Our purpose in the present paper is to study codes over finite rings using Berman's ideas. More precisely, we prove that if the code is free over an artinian local ring with finite residue field, then the code has the propriety of the singleton bound and its dimension is exactly that of its coordinatewise projection. Furthermore, a formula for the code distance of free cyclic codes over artinian local rings is established.

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