### Z_2-Triple Cyclic Codes and Their Duals

#### Abstract

A Z2-triple cyclic code of block length (

*r, s, t*) is a binary code of length*r*+*s*+*t*such 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.#### Keywords

Triple cyclic codes; minimal spanning sets; dual codes.