On the Arithmetic Complexities of Hamming Codes and Hadamard Codes
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In this paper, we study the arithmetic complexities of Hamming codes and Hadamard codes. To begin with, we present the minimum number of required exclusive-ORs (XORs) in the encoding of (punctured) Hadamard codes and (extended) Hamming codes. Then the encoding algorithms for these codes are presented to achieve the lower bound.
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