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In this paper, we investigate the encoding circuit size of Hamming codes andHadamard codes. To begin with, we prove the exact lower bound of circuit sizerequired in the encoding of (punctured)~Hadamard codes and (extended)~Hammingcodes. Then the encoding algorithms for (punctured)~Hadamard codes arepresented to achieve the derived lower bounds. For (extended)~Hamming codes, wealso propose encoding algorithms that achieve the lower bounds.

On the Exact Lower Bounds of Encoding Circuit Sizes of Hamming Codes and Hadamard Codes