Some results of linear codes over the ring $\mathbb{Z}_4+u\mathbb{Z}_4+v\mathbb{Z}_4+uv\mathbb{Z}_4$
نویسندگان
چکیده
Abstract: In this paper, we mainly study the theory of linear codes over the ring R = Z4 + uZ4 + vZ4 + uvZ4. By the Chinese Remainder Theorem, we have R is isomorphic to the direct sum of four rings Z4. We define a Gray map Φ from R n to Z 4 , which is a distance preserving map. The Gray image of a cyclic code over R is a linear code over Z4. Furthermore, we study the MacWilliams identities of linear codes over R and give the the generator polynomials of cyclic codes over R. Finally, we discuss some properties of MDS codes over R.
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