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A parametron-like ternary logic element utilizing 3rd subharmonic oscillation and 3-cycle excitation is considered. By representing the oscillation phase as a vector or phasor, the basic logical operation can be described as a majority operation for vector sum of input signals. Contrary to a delay operation of phase pi (NOT operation) in parametron, two delay operations of phase 2pi/3 and 4pi/3 need to be considered. After showing the logic design of circuits using the elements, such as multiplexsors, flip-flops, counters, etc., the structure of multiway switch based on ternary Hadamard matrix is presented and the performance of multiway switches based on ternary error-correcting codes is analyzed.