In this paper, we study cyclic codes over the ring Z p + uZ p + · · · + u k−1 Z p , where u k = 0. We find a set of generator for these codes. We also study the rank, the dual and the Hamming distance of these codes.
In this paper, we study the theory for constructing DNA cyclic codes of odd length over Z 4 [u]/u 2 which play an important role in DNA computing. Cyclic codes of odd length over Z 4 + uZ 4 satisfy the reverse constraint and the reverse-complement constraint are studied in this paper. The structure and existence of such codes are also studied. The paper… (More)
Cyclic codes over R have been introduced recently. In this paper, we study the cyclic codes over R and their Z 2 image. Making use of algebraic structure, we find the some good Z 2 codes of length 28.
Let R = F 2 + uF 2 + u 2 F 2 be a non-chain finite commutative ring, where u 3 = u. In this paper, we mainly study the construction of quantum codes from cyclic codes over R. We obtained self-orthogonal codes over F 2 as gray images of linear and cyclic codes over R. The parameters of quantum codes which are obtained from cyclic code over R are discussed.
In this paper, we develop the theory for constructing DNA cyclic codes of odd length over R = Z 4 [u]/u 2 − 1 based on the deletion distance. Firstly, we relate DNA pairs with a special 16 elements of ring R. Cyclic codes of odd length over R satisfy the reverse constraint and the reverse-complement constraint are discussed in this paper. We also study the… (More)
In this paper, we mainly study the some structure of cyclic DNA codes of odd length over the ring $R = \F_2[u,v]/\langle u^2-1,v^3-v,uv-vu \rangle$ which play an important role in DNA computing. We established a direct link between the element of ring $R$ and 64 codons by introducing a Gray map from $R$ to $R_1 = F_2 + uF_2, u^2 = 1$ where $R_1$ is the ring… (More)
The need for a motor protection system can be well understood by the fact that motors are integral device in any of the present day industries. Malfunctioning or any other faults in motor can halt the functioning of such industries. This can cause huge financial losses. So an efficient motor protection system is necessary. The present research work deals… (More)