On the Arithmetic Complexities of Hamming Codes and Hadamard Codes.
Zhengrui Li, Sian-Jheng Lin, Honggang Hu · arXiv (Cornell University) · 2018
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.