A New Method of Encoding Block Codes With Polynomials
The authors present an efficient new method of obtaining a generator matrix G from certain types of parity check matrices H with a defective cyclic block structure. This novel approach describes parity check and generator matrices in terms of polynomials. Moreover, by using this polynomial algebra they have found efficient ways to implement the scheme. In addition, this method is as such interesting as it allows them to convert H into G without a systematic encoder in between (i.e., there is no diagonal subpart in the output). This alone is striking as normally G would be dense because they have to form it from the given H by Gaussian elimination.