We analyze polarization-adjusted convolutional codes using the algebraic representation of polar and Reed-Muller codes. We define a large class of codes, called generalized polynomial polar codes which include PAC codes and Reverse PAC codes. We derive structural properties of generalized polynomial polar codes, such as duality, minimum distance. We also deduce some structural limits in terms of number of minimum weight codewords, and dimension of monomial sub-code.

翻译：本文利用极化和里德-穆勒码的代数表示方法，对极化调整卷积码进行分析。我们定义了一类广义多项式极化码，该码类包含PAC码与反向PAC码。我们推导了广义多项式极化码的结构特性，如对偶性与最小距离。同时，在最小重量码字数量与单项式子码维度方面，我们推导出若干结构极限。