Algebraic Properties of PAC Codes

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.