In this paper, a new design for an error correcting code (ECC) is proposed. The design is aimed to build an ECC circuitry with minimal power consumption. The genetic algorithm equipped with the symbiotic mechanism is used to design a power-efficient ECC which provides single-error correction and double-error detection (SEC-DED). We formulate the selection of the parity check matrix into a collection of individual and specialized optimization problems and propose a symbiotic evolution method to search for an ECC with minimal power consumption. Finally, we conduct simulations to demonstrate the effectiveness of the proposed method.