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Codes over the chain ring are obtained by writing special matrices. Gray images of these codes are binary codes. It is shown that first repeat code, second repeat code, even code and odd code are either equivalent or equal to these codes. The definitions of direct sum and direct product of these codes were given. Moreover dual codes were classed. Self dual codes and self orthogonal codes were established. Keywords : Codes over rings, Lee distance, Even codes, Odd codes, Dual codes. MSC No: 94B15, 94B60. IntroductionDifferent codes over the ring 22 u   with 2 0 u  were studied before. Generally the relation between the codes over 22 u   and binary codes were established. Some of these studies ;(1 ) u  cyclic and cyclic codes over the ring 22 u   were studied by J.F.Qian, L.N.Zhang and S.X Zhu in [3]. Some results on cyclic codes over 22 v   were studied by S. Zhu, Y. Wang and M. Shi in [9]. A relation between Hadamard codes and some special codes over 22 u   were studied by M.Özkan and F. Öke in [1]. This last study,which was written by forming special matrices over the ring is the Pioneer reference for emergance of this article. In this study, codes over the ring 22 u   are written by using special matrix. Special types of Hadamard codes ara discussed finding binary of these codes.In the second section, basic code structure was described as weigth function on the ring 22 u   and information about Hadamard codes were given. Gray map was defined. Matrices

In this study, certain matrices are obtained using the elements of a finite chain ring. Then using these matrices as generator matrices; certain codes and their duals are obtained. Moreover relations between these codes, binary codes and Hadamard codes are explained.

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Let υ be a valuation on K with value group Gυ, residue field kυ, rank υ = t and K (x1, …, xn) be the field of rational functions over K with n variables. If G is the direct sum of G1 and d infinite cyclic groups where G1 is a totally ordered group containing Gυ as an ordered subgroup with [G1 : Gυ] < ∞ and k′ is a finite field extension of kυ then there exists a residual transcendental extension u of υ to K (x1, …, xn) such that rank u = t + d, Gu = G the algebraic closure of kυ in kυ is k′ and trans deg ku/kυ = n − d.