Input bits are encoded into codewords that include coded bits. Encoding involves applying a first set of polar encoding matrices GY of prime number dimension Y to the input bits to produce output bits, and applying a second set of polar encoding matrices GZ of prime number dimension Z to the output bits to produce the codeword. One or both of GX and GY could be non-2-by-2. Such kernel design and other aspects of code construction, including reliabilities and selection of sub-channels for code construction, non-CRC-aided error correction, and code shortening and puncturing, are discussed in further detail herein.