Self-dual cyclic codes over M_2(Z_4)

07/13/2018

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by   Sanjit Bhowmick, et al.

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In this paper, we study the codes over the matrix ring over Z_4, which is perhaps the first time the ring structure M_2(Z_4) is considered as a code alphabet. This ring is isomorphic to Z_4[w]+UZ_4[w], where w is a root of the irreducible polynomial x^2+x+1 ∈Z_2[x] and U≡ 1111. We first discuss the structure of the ring M_2(Z_4) and then focus on algebraic structure of cyclic codes and self-dual cyclic codes over M_2(Z_4). We obtain the generators of the cyclic codes and their dual codes. Few examples are given at the end of the paper.