|On the Exact Lower Bounds of Encoding Circuit Sizes of Hamming Codes and Hadamard Codes
|Zhengrui Li, Sian-Jheng Lin, University of Science and Technology of China~(USTC), China; Yunghsiang S. Han, Dongguan University of Technology, China
|T.1: Complexity and Computation Theory
|Topics in Information Theory
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|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.