二进制准循环码的加法傅里叶变换编码算法

To improve the encoding efficiency of binary quasi-cyclic codes, this paper proposes a frequency domain encoding algorithm based on the additive Fourier transform. Based on the equivalence of multiplication of vectors and cyclic matrices and cyclic convolution, finite field Fourier transform is used to accelerate the cyclic convolution operation, thereby realizing fast encoding. The Lin-Chung-Han transform is selected as a tool with its convolution theorem explained. Based on the frequency domain encoding algorithm with the normal Fourier transform, it is proved that the Lin-Chung-Han transform can also be used in frequency domain encoding. To reduce the encoding complexity of binary quasi-cyclic codes, the conjugate constraint of finite field Fourier transform is used to propose the encoding algorithm for binary quasi-cyclic codes. The complexity of the given fast encoding algorithm is analyzed and compared with other algorithms. The algorithm proposed in this paper has a low complexity when the code length is long, and the transformation structure is symmetrical, which has a certain advantage in applications.