The synchronization modes of coupled relaxation electrochemical oscillators are studied. The case of ring networks of discrete electrochemical oscillators is considered where boundaries are not present. A model of discrete coupled electrochemical oscillators is derived systematically from a continuous model and a discretization procedure. It is shown that, under specific conditions, the cells are coupled electrically and the connection is linear and symmetric. Also, the coupling strength is derived explicitly as a function of the geometric network characteristics, as well as the electric properties of the surrounding medium. The model equations are studied numerically, and the different modes of synchronization are discussed in detail. It is also shown that, because of fast transitions and the elimination of phase or period differences, networks of coupled relaxation electrochemical oscillators can perform some primitive information manipulation tasks.