Derivative Descendants and Ascendants of Binary Cyclic Codes, and Derivative Decoding

This paper defines derivative descendants and ascendants of extended cyclic codes from the derivative of the Mattson-Solomon polynomials. It proves that the derivative descendants of an extended cyclic code in different directions are the same. It allows us to perform soft-decision decoding on extended cyclic codes based on the soft-decision decoding of their descendants. Simulation results show that its performance over certain extended cyclic codes, including some extended BCH codes, can be close to that of the maximum likelihood decoding.