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

In this paper, we investigate the encoding circuit size of Hamming codes and Hadamard codes. To begin with, we prove lower bounds of encoding circuit size required in the encoding of (punctured) Hadamard codes and (extended) Hamming codes. Then the encoding algorithms for (extended) Hamming codes are presented to achieve the derived lower bounds.