Construction of (2k,k, 2) Convolutional Codes with Double-Loop Cyclic Codes

In this paper, by taking multiple-time information in blocks into the coding of linear block codes, a new class of (2 \(k\) , \(k\) , 2) convolutional codes is constructed, by which a new way of constructing long codes with short ones is obtained. After that, the type of embedded codes is determined and the optimal values of the linear combination coefficients are derived by using a three-dimensional state transfer matrix to analyze and testify the constructing mechanism of the codes. Finally, the simulation experiment tests the error-correcting performance of the (2 \(k\) , \(k\) , 2) convolutional codes for different value of \(k\) , it is shown that the performance of the new convolutional codes compares favorably with that of traditional (2, 1, \(l\) ) convolutional codes.