Minimal Derivative Descendants of Cyclic Codes

This paper defines minimal derivative descendants (DDs) of an extended cyclic code from the derivative of Mattson-Solomon polynomials. It proves that the minimal DDs in different directions are equivalent codes. This allows us to perform derivative decoding based on decodings for minimal DDs with cyclic shifting. In particular, the small dimension and the large minimum Hamming distance of minimal DDs make it attractive to perform derivative decoding based on the ordered statistics decoding (OSD). Simulation results show that the derivative decoding based on the OSD can provide considerable gain.