This thesis examines two decoding methods for error correcting Reed-Solomon codes: Gao decoding and Power Decoding. We show that Gao decoding are able to correct up to $\lfloor\frac{d-1}{2} \rfloor$ errors. If the method returns a codeword this must a codeword within distance $\lfloor\frac{d-1}{2} \rfloor$ to the received message, and otherwise the method will declare failure.

Power decoding is an extension of Gao code, and for this reason it can also correct up to $\lfloor\frac{d-1}{2} \rfloor$ errors. In addition to this it can some sometimes correct more errors than this. We show examples of this as well as give some bounds on when it should not be expected to correct errors. This is also supported by simulations.

The thesis also contains a section on how to solve MgLFSR problem which is need for Power decoding.