Some results on cyclic codes over the ring R2,m

Let R-k,R-m be the ring F2(m)., [u1, u2, ... , uk]/<ui2,,ujuj-ujui). In this paper, cyclic codes of arbitrary length n over the ring R-2,R-m are completely characterized in terms of unique generators and a way for determination of these generators is investigated. A F-2(m), -basis for these codes is also derived from this representation. Moreover, it is proven that there exists a one-to-one correspondence between cyclic codes of length 2n, 71 odd, over the ring Rk-1,m and cyclic codes of length n over the ring R-k,R-m. By determining the complete structure of cyclic codes of length 2 over R-2,(m), a mass formula for the number of these codes is given. Using this and the mentioned correspondence, the number of ideals of the rings R-2,R-m and R-3,R-m,, is determined. As a corollary, the number of cyclic codes of odd length n over the rings R-2,R-m and R-3,R-m is obtained.