(untitled) (European Journal of Pure and Applied Mathematics, 2017)
A Z2-triple cyclic code of block length (r, s, t) is a binary code of length r + s + t suchÂ that the code is partitioned into three parts of lengths r, s and t such that each part is invariant under the cyclic shifts of the coordinates. Such a code can be viewed as Z2[x]-submodules of Z_2[x]/<x^r-1>*Z_2[x]/<x^s-1>*Z_2[x]/<x^t-1>, in polynomial representation. In this paper, we determine the structure of these codes. We have obtained the form of the generators for such codes. Further, a minimal generating set for such codes is obtained. Also, we study the structure of the duals of these codes via the generators of the codes.