Systems and methods are disclosed for performing rate matching when using general polar codes. In one embodiment, a method of generating a codeword includes receiving bits at a polar encoder and encoding the bits using polar encoder kernels. The polar encoder kernels include a first kernel and a second kernel. The first kernel receives a set of input q-ary symbols and modifies the set of input q-ary symbols according to a first kernel generator matrix to produce a set of output q-ary symbols. The second kernel receives a set of input l-ary symbols, where l does not equal q, and modifies the set of input l-ary symbols according to a second kernel generator matrix to produce a set of output l-ary symbols. For example, the first kernel may be a binary kernel and the second kernel may be a Reed-Solomon (RS) based kernel.