Quadratic residue (QR) codes have a high prospect on error correction for reliable data conveyance over channel with noise. This paper presents a fast algebraic scheme for decoding the binary (41, 21, 9) QR code for correcting up to 4 errors on an one-case-by-one-case basis, in which the calculation of unknown syndromes is eliminated and the conditions for checking for the various numbers of errors that exist in the received word are also simplified compared to those from Lin T. C. et al.’s algorithm, which is a traditional algebraic decoding algorithm (ADA). The computational complexity of the decoder performing the binary (41, 21, 9) QR code is analyzed thoroughly, which demonstrates that the proposed decoding scheme is faster, simpler, and more suitable for implementation than Lin T. C. et al.’s algorithm. Numerical emulation results demonstrate that the proposed decoding scheme achieves the same error-rate performance as Lin T. C. et al.’s algorithm, but it has a significantly decreased the complexity of this decoder in terms of the CPU time.

二次余数（QR）码在纠错方面具有很高的前景，可以在带有噪声的通道上可靠地传输数据。本文提出了一种快速的代数方案，用于对二进制（41、21、9）QR码进行解码，以逐一纠正多达4个错误，其中消除了未知校验子的计算，并且与林TC等人的算法（传统的代数解码算法（ADA））相比，检查接收到的单词中存在的各种错误数量的条件也得到了简化。彻底分析了执行二进制（41、21、9）QR码的解码器的计算复杂度，这表明与Lin TC等人相比，所提出的解码方案更快，更简单并且更适合于实现。的算法。数值仿真结果表明，所提出的解码方案具有与Lin TC等人的算法相同的误码率性能，但是就CPU时间而言，它大大降低了该解码器的复杂度。