Abstract：In order to reduce the computational complexity of computing unknown syndromes for the coefficients of the error-locator polynomial and reduce the decoding time when one is decoding, this paper proposed an algebraic decoding algorithm of (41, 21, 9) QR code without calculating the unknown syndromes
by solving the Newtonian identity. Simultaneously, an objective theoretical analysis of the computational complexity is given for the part of improvement. Besides, this paper also puts forward the simplifying conditions to determine the number of errors in the received word, which in order to further reducing the decoding time. Simulation results show that the proposed algorithm reduces the decoding time with maintaining the same decoding performance of Lin’s algorithm
