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In realization of recursive digital filters with fixed point arithmetic, an error caused by roundoff arises and the error feedback (EF) is an effective method to reduce the roundoff noise. It is desirable to design the EF using as few parameters as possible in order to keep costs low. In this paper, we propose a design method of 2D EF network under some constraints. Here, to reduce the cost, we propose some EF coefficients sets and let the elements have the same absolute value. In order to optimize the coefficients sets, we propose an algorithm by using the genetic algorithm (GA). In the numerical example, we demonstrate the effectiveness of the proposed method.