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Malaysian Journal of Science, Volume 34, Issue 2, 2015, pp. 222-226

For codes over fields, the MacWilliams equivalence theorem give us a complete characterization when two codes are equivalent. Considering the important role of the Lee weight in coding theory, one would like to have a similar results for codes over integer residue rings equipped with the Lee weight. We would like to prove that the linear isomorphisms between two codes in ℤ_{n}^{m} that is preserving the Lee weight are exactly the maps of the form f(x_{1},x_{2},...,x_{m}) = (u_{1}x_{σ(1)},u_{2}x_{σ(2)},...,u_{m}x_{σ(m)}) where u_{1},...,u_{m} ∈ {-1,1} and σ ∈ S_{n}. The problem is still largely open. Wood proved the result for codes over ℤ_{n} where n is a power of 2 or 3. In this paper we prove the result for prime n of the form 4p+1 where p is prime.