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Reed-Solomon (RS) codes are adopted in many digital communication and storage systems to ensure data reliability. For many of these systems, the encoder and decoder are not active at the same time. In previous designs, RS encoders implemented as linear feedback shift registers in a concatenated structure are reused to compute the syndromes so that the decoder complexity is reduced. However, the parallel versions of such encoders have very long critical path and hence can not achieve high speed. This paper proposes a new parallel resource-shareable RS encoder architecture based on the Chinese Remainder Theorem (CRT). The generator polynomial of RS codes is decomposed into factors of degree one and state transformation is developed to enable the sharing of the hardware units for syndrome computation. As a result, the critical path is reduced to only one multiplier and one adder, regardless of the parallelism. Additionally, by utilizing the property that the degrees of the decomposed polynomial factors are one, optimizations are also developed to greatly simplify the CRT-based encoder. For example encoders of a (255, 229) RS code over GF(2^8), our proposed design can achieve at least 29% higher efficiency in terms of area-time product for moderate or higher parallelisms compared to the previous resource-shareable RS encoder and traditional parallel RS encoders combined with syndrome computation units that implement the same functionality.